ERCIYES UNIVERSITY - Fen FakÃ¼ltesi - Erciyes Ãniversitesi

ERCIYES UNIVERSITY 

FACULTY OF SCENCES 

DEPARTMENT OF MATHEMATICS 

I. GENERAL INFORMATION 

Course Title M101 Analaysis I 

Semester: Fall Smester Language: Turkish 

Local Credit (T-P-C) : 4 25 ECTS Credit: 9 

Instructor Asist. Prof. Abdulcabbar SÖNMEZ 

Office Hour Friday 14.00-15.00 

Email: sonmez@erciyes.edu.tr WEB: 

Erciyes University 

Faculty of Arts and Sciences 

Department of Mathematics 

38039-Kayseri /TURKEY 

Phone: 90 352 4374937 / 33217 

Fax: 90 352 4374933 

II. COURSE INFORMATION 

The Type and Level of Course 

Must: Yes Elective: 

Core Yes Related: Minor 

Elementary: Intermediate: Advanced: Specialized: 

Yes 

Course Content Sets,Functions,Limit, continuity, differentiation 

Course Objective Give students the basic concepts that are used in all areas of 

mathematics and to teach them. 

Books The following books are recommended : 

1. M.Balcı, Matematik Analiz, Balcı Yayınları,Ankara,2008 

2. Tom M.Apostol, Mathematical Analysis, Addison-Wesley 

Publ.Company, London, 1973.. 

3. W.Rudin, Principles of Mathematical Analysis, McGraw-Hill, New 

York, 

4.Berki Yurtsever,Matematik Analiz Dersleri I Ankara 1978. 

Student 

Responsibility 

To be successful the students have to continue to lessons to repeat the 

topics at home to make homework given at the end of topics and to 

repeat generally all topics at the exam periods .

Weekly schedule 

WEEK 

CHAPTER TOPICS 

1 Sets, Numbers and examples. 

2 Linear point sets , theorems ,examples, 

3 The concept of function and examples, 

4 The concept of countability , examples and introduction to sequences 

5 Sequences and related theorems, Cauchy sequences. 

6 Limit of the sequences and examples 

7 Continious function and its properties 

8 Theorems related to continious functions and their examples 

9 The concept of derivative , The relationship between derivative and contiuity. 

10 MIDTERM EXAM 

Rules of differentiation 

11 

12 Differentiation of trigonometric and composite functions ,examples 

13 

Differentiation of inverse, exponential and logarithmic functions ,examples 

14 Logarithmic differentiation ,derivative of hyperbolic funtions ,high-order 

derivatives and examples 

15 FINAL EXAM 

Öneren Öğretim Üyesi 

Asist. Prof. Abdulcabbar SÖNMEZ 

Öneren Anabilim Dalı Başkanı 

Prof. Dr. Fuat Gürcan





Course Title M102 Analaysis II 

Semester: Spring Smester Language: Turkish 

Local Credit (T-P-C) : 4 2 5 ECTS Credit: 9 


Office Hour Friday: 13:00-14:00 






Phone: 90 352 4374937 / 33217 

Fax: 90 352 4374933 






Yes 

Course Content Theorems about derivative,Indeterminate Forms ,Curve sketching, 

Indefinite Integrals, Definite Integrals, Applications of Definite 

Integrals 

Course Objective Give students the basic concepts that are used in all areas of 

mathematics and to teach them. 


1. M.Balcı, Matematik Analiz, Balcı Yayınları,Ankara,2008 

2. Tom M.Apostol, Mathematical Analysis, Addison-Wesley 

Publ.Company, London, 1973.. 

3. W.Rudin, Principles of Mathematical Analysis, McGraw-Hill, New 

York, 

4.Berki Yurtsever,Matematik Analiz Dersleri I Ankara 1978. 

Student 






WEEK 

1 


Theorems about derivative and their application 

2 Indeterminate Forms and Their Applications 

3 Graph Sketching 

4 Indefinite Integrals 

5 Techniques of integration 

6 Binomial Integrals 

7 Definite Integrals , Partitition of Intervals ,Step functions and their integrals 

8 Riemann Integral and Related theorems 

9 Classes of Integrable Functions 


11 Calculation of some limits with the help of integral 

12 Area calculation as an application of definite integral 

Arclength and volume calculation 

13 

14 Areas of Surfaces of Revolution 

15 FINAL EXAM 






FACULTY OF SCIENCES 



Course Title M105 Abstract Mathematics and Logic I 

Semester: Autumn Term Language: Turkish 


Instructor 

Asist. Prof. A. Nihal TUNCER 


Email: ntuncer@erciyes.edu.tr 

WEB: 


Faculty of Sciences 



Phone: 90 352 4374937 / 33218 

Fax: 90 352 4374933 



Must: 

Elective: Yes 


Elementary: Intermediate: Advanced: Yes Specialized: 

Course 

Content Symbolic Logic, Concept of set , Relations, Set algebra. 

Course 

Objective 

This course prepares the fundamentals of the courses given between the 3. 

and 8. semesters. 

Books Following books are recommended to the student: 

• Soyut Matematik, S. Akkaş, H. H. Hacısalihoğlu, Z. Özel, A. 

Sabuncuoğlu, Gazi Üniversitesi yayın No. 124, 1. Baskı (1984) 

• Çözümlü Soyut Matematik Problemleri, S.Akkaş, H.H.Hacısalihoğlu, 

Z. Özel, A. Sabuncuoğlu, Gazi Üniversitesi yayın No. 124, 1. Baskı 

(1988) 

• Örneklerle Soyut Matematik, Fethi Çallıalp, 3. Baskı, İstanbul 1999. 

• Introduction to Modern Algebra, M. Larsen, Addison-Wesley 

Pub. Reading Mass. 1969. 

Student 


To be successful the students have to continue to lessons to repeat the topics 

at home to make homework given at the end of topics and to repeat 

generally all topics at the exam periods .

Weekly Schedule 

WEEK 


1 Symbolic Logic 

2 Equivalent statements,converse of a statement, composite statements 

3 Propositional formula,Logical equivalence,totologies 

4 Fundemental principles,application of topic 

5 Proving Strategies for theorems 

6 Concept of set and element,representation of sets 

7 Subset,union of sets ,intersection of sets and their applications 

Complement of a set,difference of two sets,symmetric difference and their 

8 

applications 

9 Family of sets ,concept of finite and infinite sets 


11 Power set of a set,separation of sets ,cover of sets 

12 Ordered pair,ordered n-tuple,Cartesian product of sets,relation 

13 Properties of relation, equivalence relation,equivalence classes 

14 Order relation and applications 

FINAL EXAM





Course Title M106 Abstract Mathematics and Logic II 

Semester: Spring Term Language: Turkish 


Instructor 

Asist. Prof. A. Nihal TUNCER 



WEB: 





Phone: 90 352 4374937 / 33218 

Fax: 90 352 4374933 





Elementary: Yes Intermediate: Advanced: Specialized: 

Course Content 

Functions,operation,Mathematical Structures,Natural Numbers, 

Integers, Rational Numbers, Real Numbers, Complex Numbers. 

Course Objective This course gives the funndementals of the courses given between the 

3. and 8. semesters. 

Books 

Following books are recommended to the student: 

• Soyut Matematik, S. Akkaş, H. H. Hacısalihoğlu, Z. Özel, A. 

Sabuncuoğlu, Gazi Üniversitesi yayın No. 124, 1. Baskı (1988) 

• Çözümlü Soyut Matematik Problemleri, S.Akkaş, 

H.H.Hacısalihoğlu, Z. Özel, A. Sabuncuoğlu, Gazi Üniversitesi 

yayın No. 124, 1. Baskı (1988) 

• Örneklerle Soyut Matematik, Fethi Çallıalp, 3. Baskı, İstanbul 

1999 

• Introduction to Modern Algebra, M. Larsen, Addison-Wesley 

Pub. Reading Mass. 1969 

Student 


To be successful the students have to continue to lessons , to repeat 

the topics at home , to make homework given at the end of topics and 

to repeat generally all topics at the exam periods .


WEEK 


1 Definition of function 

2 Types of functions and applications 

3 Operation and applications 

4 Mathematical structures,group and ring 

5 Vector space,field,algebra and related applications 

6 Natural numbers 

7 Induction principle and related applications 

8 İntegers,Order on integer set and related applications 

9 Rational numbers and related applications 

10 MİDTERM EXAM 

11 Real numbers ,concept of sequence , cauchy sequence and completeness 

12 Irrational numbers and complex numbers 

13 Polar representation of complex numbers ,exponential form 

14 Complex powers and related applications 

FINAL EXAM





Course Title M 107 Linear Algebra I 



Instructor 

Prof. Dr Himmet CAN 


Email: can@erciyes.edu.tr 

WEB: 





Phone: 90 352 4374937 / 33210 

Fax: 90 352 4374933 






Course Content Sets, Some properties of Z, The division algorithm, Highest common 

factors and Euclid’s algorithm, Equivalence relations, Mappings, 

Groups and subgroups, Period of an element, Cyclic groups, Cosets 

and Lagrange’s theorem on finite groups, Normal subgroups, Quotient 

groups, Homomorphisms and their elementary properties , Kernel and 

image, Isomorphism theorems, Direct products of groups. 

Course Objective The main objective of the course is to provide the students with the 

knowledge about sets, the fundamental properties of Z, equivalence 

relations, mappings and group theory, so that the students will be 

ready for more intermediate topics in the course of linear algebra 

given at first spring term. 

Books 


1. H. H. HACISALİHOĞLU, Lineer Cebir, Fırat Üniversitesi, 

Fen Fakültesi Yayınları, İstanbul, 1982. 

2. J. A. GREEN, Sets and Groups: A first course in algebra, 

Routledge and Kegan Paul, London and New York, 1988. 

3. T. A. WHITELAW, An Introduction to Abstract Algebra, 

Blackie, Glasgow and London, 1978.

Student 


4. G. BIRKHOFF and S. MAC LANE, A Survey of Modern 

Algebra, Macmillan, New York, 1967. 

To be successful the students have to continue to lessons (40 hours), 

to repeat the topics at home (20 hours), to make homework (5 

homeworks) given at the end of topics (20 hours) and to repeat 

generally all topics at the exam periods (20 hours). 


WEEK 


1 Sets and subsets. 

2 Some properties of Z, The division algorithm. 

3 Highest common factors and Euclid’s algorithm. 

4 Equivalence relations and equivalence classes. 

5 Mappings and permutations. 

6 Groups and examples of groups. 

7 Subgroups and some important general examples of subgroups. 

8 MID-TERM EXAM 

9 Period of an element, Cyclic groups. 

10 Cosets and Lagrange’s theorem on finite groups. 

11 Normal subgroups, Quotient groups. 

12 Homomorphisms and their elementary properties. 

13 Isomorphic groups, Kernel and image. 

14 Isomorphism theorems, Direct product of groups. 

15 FINAL EXAM 


Himmet CAN 







Course Title M 108 Linear Algebra II 



Instructor 




WEB: 





Phone: 90 352 4374937 / 33210 

Fax: 90 352 4374933 





Elementary: Intermediate: Yes Advanced: Specialized: 

Course Content Ring and field, Vector spaces, Linear mappings, Matrices, Systems of 

linear equations, Determinants, Inner product spaces. 

Course Objective This course aims to teach the student the fundamental concepts of 

linear algebra such as vector spaces, linear mappings, matrices, 

systems of linear equations, determinants and inner product spaces. 

Books 


Student 


1. H. H. HACISALİHOĞLU, Lineer Cebir, Fırat Üniversitesi, 

Fen Fakültesi Yayınları, İstanbul, 1982. 

2. J. A. GREEN, Sets and Groups: A first course in algebra, 

Routledge and Kegan Paul, London and New York, 1988. 

3. S. I. GROSSMAN, Elementary Linear Algebra, Wadsworth 

Publishing Company, California, 1987. 

4. K. SPINDLER, Abstract Algebra with Applications, Marcel 

Dekker, New York, 1994. 

5. V. V. Prasolov, Problems and Theorems in Linear Algebra, 

AMS, 1996. 




generally all topics at the exam periods (20 hours).


WEEK 


1 Ring and field. 

2 Vector spaces and subspaces. 

3 Bases and dimension. 

4 Linear mappings, Isomorphisms, Image and kernel. 

5 Matrices. 

6 Rank and equivalence. 

7 Systems of linear equations, Matrix inversion. 


9 Matrices and linear mappings. 

10 Determinants. 

11 Inner products. 

12 Orthogonal and orthonormal bases. 

13 The characteristic polynomial, Eigenvalues and eigenvectors. 

14 Cayley- Hamilton theorem. 

15 FINAL EXAM 


Himmet CAN 




FACULTY OF ARTS AND SCENCES 

DEPARTMENT OF PHYSICS 


Course Title MATFİZ101 Physics I (Mechanics) 

Semester: Autumn term Language: Turkish 


Instructor 

Prof. Dr. Necmettin MARAŞLI 

Office Hour Monday /Tuesday /Wednesday /Thursday/ Friday 14.00-14.30 

Email: marasli@erciyes.edu.tr 

WEB Site: 



Department of Physics 


Phone: 90 352 4374901 Extn. 33114 

Fax: 90 352 4374933 




Core: Yes Related: Minor: 


Course Content Physics and measurement, Vectors, Motion in one dimension, Motion 

in two dimensions, The laws of motion, Circular motion and other 

applications of Newton’s Laws, Work and energy, Potential energy 

and conservation of energy, Linear momentum, Collisions, 

Equilibrium of rigid bodies and problem solving 

Course Objective The purpose of this course is to provide the student with a clear 

presentation of the theory and application of the principles of physics 

laws and to develop students’ ability to analyze problems based on the 

understanding of its basic concepts. 

Books 

Following books are recommended: 

* Fen ve Mühendislik için Fizik I, R. A. Serway et al, Palme Press, 

2002 (Translation editor: K. Çolakoğlu). 

* Fiziğin Temelleri I, D. Halliday, R. Resnick, Arkadaş Press, 2nd 

Press, 1991, (Translation: Cengiz Yalçın). 

* Temel Fizik I, P. M. Fisbane, Arkadaş Press, 2003 (Translation: 

Cengiz Yalçın). 

Student 


To be present at the lessons (4x14=56 hours), to repeat the topics at 

home (1.5x14=21 hours), to make home works and to endeavor to 

solve the problems (1.5x14=21 hours) and to overview generally all 

topics related to the exams. (0.5x14=7 hours). 

(Total 105 hours/25 = 4.2 ECTS)


WEEK 


1 Physics and measurement 

2 Vectors 

3 Motion along a straight line 

4 Motion in a plane 

5 Newton’s laws of motion 

6 Dynamic of circular motion 

7 Work and kinetic energy 


9 Potential energy and conservation of energy 

10 Momentum and conservation of momentum 

11 Collisions 

12 The rotational motion 

13 Dynamic of rotational motion 

14 Static equilibrium 

FINAL EXAM



DEPARTMENT OF PHYSICS 


Course Title MATFİZ102 Physics II (Electric and Magnetism) 

Semester: Spring term Language: Turkish 


Instructor 

Prof. Dr. Necmettin MARAŞLI 

Office Hour Monday /Tuesday /Wednesday /Thursday/ Friday 14.00-14.30 

Email: marasli@erciyes.edu.tr 

WEB Site: 



Department of Physics 


Phone: 90 352 4374901 Extn. 33114 

Fax: 90 352 4374933 






Course Content Electrical charge and electric field, Electric flux, Gauss’s law and its 

applications, Electrical potential, Capacitors and dielectrics, Current 

and resistance, Direct current circuits, Kirchhoff’s laws, The magnetic 

field, Sources of magnetic field, Magnetic induction, Faraday’s law, 

Maxwell’s laws and problem solving. 

Course Objective The purpose of this course is to provide the student with a clear 

presentation of the theory and application of the principles of electric 

and magnetism laws and to develop students’ ability to analyze 

problems based on the understanding of its basic concepts. 

Books 

Following books are recommended: 

* Fen ve Mühendislik için Fizik II, R. A. Serway et al, Palme Press, 

2002 (Translation editor: K. Çolakoğlu). 

* Fiziğin Temelleri II, D. Halliday, R. Resnick, Arkadaş Press, 2nd 

Press, 1991, (Translation: Cengiz Yalçın). 

* Temel Fizik II, P. M. Fisbane, Arkadaş Press, 2003 (Translation: 

Cengiz Yalçın). 

Student 


To be present at the lessons (4x14=56 hours), to repeat the topics at 

home (1.5x14=21 hours), to make home works and to endeavor to 

solve the problems (1.5x14=21 hours) and to overview generally all 

topics related to the exams. (0.5x14=7 hours). 

(Total 105 hours/25 = 4.2 ECTS)


WEEK 


1 Electric charge and Coulomb’s Law 

2 Calculations of electric field 

3 Electric flux and Gauss’s law 

4 Applications of Gauss’s law 

5 Electrical potential 

6 Capacitors and dielectrics 

7 Current and resistance 


9 Direct current circuits 

10 Kirchhoff’s laws 

11 The magnetic field and magnetic forces 

12 Sources of magnetic field 

13 Magnetic Induction 

14 Faraday’s Law and Maxwell’s equations 

FINAL EXAM





Course Title M 202 Analysis IV 



Instructor 

Prof. Hikmet ÖZARSLAN 

Office Hour Thursday 10.00-12.00 

Email: seyhan@erciyes.edu.tr 

WEB: 





Phone: 90 352 4374937 / 33209 

Fax: 90 352 4374933 






Course Content Improper Integrals, Multivariable functions and their limit, Continuity 

and Differentiability of Multivariable Functions , Composite 

Functions,Implicit Functions, Extreme Values, Line Integrals,Multiple 

Integrals and Their Applications 

Course Objective To help students learn the concept of functions of several variables 

thoroughly and to enhance their awaraness on the concepts of limit 

,continuity,differentiation,integration etc. 

Books 


• Berki YURTSEVER, Matematik Analiz Dersleri, Cilt I, Ankara 1968. 

• Mustafa BALCI, Matematik Analiz, Cilt II, Ankara 1997. 

• H. Hacı Hilmisalihoğlu, Temel ve Genel Matematik, Cilt I, 

Ankara. 

• Ahmet A. KARADENİZ,Yüksek Matematik, Cilt II, İstanbul 

1985. 

• Abdulkadir ÖZDEĞER-Nursun ÖZDEĞER, Çözümlü Yüksek 

Matematik Problemleri, Cilt I, İstanbul 1994. 

• Abdulkadir ÖZDEĞER-Nursun ÖZDEĞER, Çözümlü Yüksek 

Matematik Problemleri, Cilt II, İstanbul 1996. 

• S. C. MALİK, Mathematical Analysis, 1984. 

Student 



the topics at home , to make homework given at the end of topics, 

and to repeat generally all topics at the exam periods .


WEEK 


1 Improper Integrals 

2 Convergence Tests for Improper Integrals 

3 Domains of multivariable functions 

4 Limit and Continuity of Multivariable Functions 

5 Partial Differentiation of Multivaribale Functions 

6 Higher order Partial Derivatives 

7 Differentiability of Multivaribale Functions and Exact Differential 

8 Directional Derivative ,Gradient,Divergence and Curl 

9 Composite Functions and Implicit Functions 


11 Domain Transformations and Composite Transformations 

12 Mean Value Theorem and Taylor Formula for Multivariable Functions 

13 Extreme Values for Multivariable Funtions 

14 Double integrals and their applications 

FINAL EXAM





Course Title M 201 Analysis III 


Local Credit (T-P-C) 4 0 4 ECTS Credit: 8 

Instructor 




WEB: 





Phone: 90 352 4374937 / 33209 

Fax: 90 352 4374933 






Course Content Infinite series with positive terms and their convergence tests, 

Decreasing series with positive terms and their convergence tests, 

Series with arbitrary terms and their convergence tests , 

Multiplication of infinite series,Power Series, Series and sequences 

with variable terms, Uniform convergence tests for series with 

variable terms 

Course Objective Aim of this course is to help students learn series by establising 

connections with the sequences , to help them develop the ability of 

calculating infinite sums and determining their convergence character. 

Books 


Student 


• Berki YURTSEVER, Matematik Analiz Dersleri, Cilt I, Ankara 1968. 

• Mustafa BALCI, Matematik Analiz, Cilt II, Ankara 1997. 

• H. Hacı Hilmisalihoğlu, Temel ve Genel Matematik, Cilt I, 

Ankara. 

• Ahmet A. KARADENİZ,Yüksek Matematik, Cilt II, İstanbul 

1985. 

• Abdulkadir ÖZDEĞER-Nursun ÖZDEĞER, Çözümlü Analiz 

Problemleri, Cilt II, İstanbul 1994 

• S. C. MALİK, Mathematical Analysis, 1984 

To be successful the students have to continue to lessons, to repeat the 

topics at home , to make homework given at the end of topics and to 



WEEK 


1 Infinite Series and their convergence 

2 Infinite Series with positive Terms and their convergence tests 

3 Decreasing series with positive terms and their convergence tests 

4 Series with arbitrary terms 

5 Convergence tests for the series with arbitrary terms 

6 Numerical calculation of series and error ,remainder estimation 

7 Multiplication of infinite series 

8 Power series 

9 Sequences with variable terms 


11 Series with variable terms 

12 Uniform convergence of a sequence with variable terms 

13 Uniform convergence of a serie with variable terms 

14 Uniform convergence tests for series with variable terms 

FINAL EXAM



DEPARTMENT OF MATHEMATİCS 

I. GENEL BİLGİLER 

Ders Adı 

MAT 203 General Topology I 

Dönemi: Güz Dili: Türkçe 

Kredisi (T-P-K) : 4 0 4 ECTS Kredisi: 6 

Öğretim Üyesi Prof. Dr. Mehmet Baran 

Görüşme Saatleri 

E posta: baran@erciyes.edu.tr 

WEB: 

Erciyes Üniversitesi 

Fen Edebiyat Fakültesi 

Matematik Bölümü 

38039-Kayseri / TURKİYE 

Tel: 90 352 4374937 / 33206 

Faks: 90 352 4374933 

II. DERS BİLGİLERİ 

Ders Tipi ve Seviyesi 

Zorunlu: 

Seçmeli: Evet 

Esas: Evet İlgili: Yan dal: 

Başlangıç: Orta: Evet İleri: Uzmanlık: 

Ders İçeriği Sets, relations, functions, cauntable sets, topological spaces, open sets, 

neighborhoods, closed sets, accumulation points, closure of a set, 

ınterior, exterior, boundary, sequences, subspaces, bases and subbases. 

Amaç 

Kitaplar • G. Preuss, Foundations of Topology, Kluwer Academik 

Publisher, 2002. 

• S., Lipshutz, General Topology, Mcgraw-Hill, 1965. 

• O., Mucuk, Topoloji ve Kategori, Nobel Yayın, 2010. 

• G. Aslım, Genel Topoloji, Ege Üniv. Fen Fak. Yayın., 2004. 

Öğrenci 

Sorumluluğu

HAFTALIK DERS PLANI 

Anlatılacak Konuların Dönemlik Dağılımı 

1. Hafta Sets, relations 

2. Hafta functions, cauntable sets 

3. Hafta topological spaces 

4. Hafta examples, theorems 

5. Hafta open sets 

6. Hafta neighborhoods, closed sets 


8. Hafta Mid-term exam 

9. Hafta accumulation points 

10. Hafta closure of a set, ınterior, exterior, boundary 


12. Hafta 

sequences, subspaces 

13. Hafta bases and subbases 


15. Hafta Final Exam




I. GENEL BİLGİLER 

Ders Adı 

MAT 204 General Topology II 

Dönemi: Güz Dili: Türkçe 

Kredisi (T-P-K) : 4 0 4 ECTS Kredisi: 6 

Öğretim Üyesi Prof. Dr. Mehmet Baran 

Görüşme Saatleri 

E posta: baran@erciyes.edu.tr 

WEB: 

Erciyes Üniversitesi 

Fen Edebiyat Fakültesi 

Matematik Bölümü 

38039-Kayseri / TURKİYE 

Tel: 90 352 4374937 / 33206 

Faks: 90 352 4374933 

II. DERS BİLGİLERİ 

Ders Tipi ve Seviyesi 

Zorunlu: 

Seçmeli: Evet 

Esas: Evet İlgili: Yan dal: 

Başlangıç: Orta: Evet İleri: Uzmanlık: 

Ders İçeriği Continuous functions, open and closed functions, homeomorphic 

spaces, topological properties, metric spaces, metric topology, 

equivalent metrics, normed spaces, the initial and final topologies, 

product spaces and quotient spaces. 

Amaç 

Kitaplar • G. Preuss, Foundations of Topology, Kluwer Academik 


• S., Lipshutz, General Topology, Mcgraw-Hill, 1965. 



Öğrenci 

Sorumluluğu



1. Hafta Continuous functions 

2. Hafta open and closed functions 

3. Hafta homeomorphic spaces 


5. Hafta topological properties 

6. Hafta metric spaces 


8. Hafta Mid-term exam 

9. Hafta metric topology, equivalent metrics 

10. Hafta normed spaces 


12. Hafta 

13. Hafta 

the initial and final topologies 

product spaces and quotient spaces 


15. Hafta Final Exam





Course Title MAT 205 Analytic Geometry I 



Instructor 

Prof.Dr.Mehmet ÖZDEMİR 


Email: ozdemirm@erciyes.edu.tr 

WEB: 





Phone: 90 352 4374937 / 33207 

Fax: 90 352 4374933 






Course Content Vector spaces,Metric properties of R 2 and R 3 vector 

spaces,Calculations of area and volume, Coordinate roofs and 

coordinate systems,Line equation , Line equation in space,Plane 

equations,Line-plane relations,Analysis of planes,Reflections. 

Course Objective The aim of this course is to give basic concepts and theorems of 

Analytic Geometry. 

Books 

Following books are recommended. 

• AnalitikGeometri,Prof.Dr.H.H.Hilmihacısalihoğlu,Ankara 

Üniv.Fen Fak.Yayınları,1998. 

• AnalitikGeometri,Prof.Dr.RüstemKaya,AnadoluÜniv.Fen 

Fak.Yayınları,1985. 

Student 



to repeat the topics at home (28 hours) to make homework (5 

Homework) given at the end of topics, (10 hours) and to repeat 

generally all topics all exam periods. (10 hours) (Total 6 ECTS) 


WEEK 


1 Vector spaces, 

2 Metric properties of R and R vector spaces, 

3 Calculations of area and volume,

4 Coordinate roofs and coordinate systems, 

5 Coordinate systems, 

6 Line equation, 

7 Line equation 


9 Line equation in space, 

10 Plane equations, 

11 Line-plane relations, 

12 Line-plane relations, 

13 Analysis of planes, 

14 Reflections.. 

FINAL EXAM





Course Title MAT 206 Analytic Geometry II 



Instructor 

Prof.Dr.Mehmet ÖZDEMİR 


Email: ozdemirm@erciyes.edu.tr 

WEB: 





Phone: 90 352 4374937 / 33207 

Fax: 90 352 4374933 






Course Content Translations in plane Geometry and Rotations, Conics, Second order 

Surfaces and Classification Ellipsoid, Hyperboloid and Hyperbolic 

paraboloid, Graph of the Curves. 


Analytic Geometry. 

Books 


• AnalitikGeometri,Prof.Dr.H.H.Hilmihacısalihoğlu,Ankara 

Üniv.Fen Fak.Yayınları,1998. 

• AnalitikGeometri,Prof.Dr.RüstemKaya,AnadoluÜniv.Fen 

Fak.Yayınları,1985. 

Student 







WEEK 


1 Translations in plane Geometry and Rotation, 

2 Translations in plane Geometry and Rotation, 

3 Conics,Circle 

4 Conics,The Ellipse,

5 The parabola, 

6 The Hyperbola, 

7 Second order surfaces and Classification, 


9 Second order surfaces and Classification, 

10 Hyperboloid, 

11 Elliptical and Hyperbolic Paraboloid, 

12 Graph of the curves, 

13 Graph of the curves, 

14 Graph of the curves. 

FINAL EXAM





Course Title M 211 Number Theory I 

Semester: Fall Term Language: Turkish 


Instructor Prof. Dr. Hüseyin Altındiş 


Email: altindis@erciyes.edu.tr WEB Site: 


Faculty of Science 

Department of …Mathematic 

38039-Kayseri / TURKEY 

Phone: 90 352 4374937 / 33205………. 

Fax: 90 352 4374933 






Course Content The İntegers and Properties,The Division Algorithm, Representations 

of İntegers, Divisibility, GCD,LCM and Aplications, Linear 

Diophantine Equations, Arithmetic Functions, Congruences. 

Course Objective Give the basic issues of elementary-level of Number Theory 

Books Number Theory and its Appl.,Laser Ofset,Ankara, 2005. 

Student 


To be successful the students have to continue to lessons (56 hours), to 

repeat the topics at home (28 hours) to make homework (5 Homework) 

given at the end of topics, (10 hours) and to repeat generally all topics 

all exam periods. (10 hours) 


WEEK 


1 The İntegers and Properties,The Division Algorithm 

2 Base Arithmetic 

3 Divisibility 

4 GCD 

5 LCM 

6 GCD and LCM’s Aplications 

7 Linear Diophantine Equations 


9 Linear Diophantine Equation Systems 

10 Arithmetic Functions 

11 The Euler Totient (Q) Function, The Möbius Function

12 Definition and Properties of Congruence 

13 Congruence Equations 

14 Congruence Aplications 

FINAL EXAM





Course Title M 212 Number Theory II 



Instructor Prof. Dr. Hüseyin Altındiş 


Email: altindis@erciyes.edu.tr WEB Site: 


Faculty of Science 



Phone: 90 352 4374937 / 33205………. 

Fax: 90 352 4374933 






Course Content Systems of linear Congruences, The Chinese remainder theorem, 

Systems of n unknowns linear Congruances, Non Linear Congruances, 

Primitive roots, Indices, Quadratic residues, Continued fractions. 

Course Objective 

Books Number Theory and its Appl. , Berdan, Istanbul 1999 

Student 





all exam periods. (10 hours) (Total 104 hours/25 = 4 ECTS) 


WEEK 


1 Systems of linear Congruences, The Chinese remainder theorem 

2 Systems of n unknowns linear Congruances 

3 Non Linear Congruances, Theorems of Lagrange and Wilson 

4 The order of an integer, Primitive roots 

5 Indices 

6 Applications of Primitive roots and Indices 

7 Quadratic residues, The Legendre symbol, Euler’s criterion 


9 Gauss’ Lemma, The Quadratic Reciprocity Law 

10 Quadratic Congruences, The Jacobi symbol 

11 Finite Continued fractions 

12 Infinite Continued fractions

13 Periodic Continued fractions 

14 Applications of the Continued fractions 

FINAL EXAM





Course Title M213 Set Theory I 



Instructor 

Office Hour 

Email: 

WEB: 





Phone: 90 352 4374937 / 33201 

Fax: 90 352 4374933 



Must: 

Elective: Yes 



Course Content Naive set theory, Logical axioms and inference rules, Axioms of set 

theory, order pairs, related Functions, equality relations, order 

relations, order type, well order sets, partial and completed order sets, 

order numbers, finite induction, finite and infinite sets. 

Course Objective To understand foundamentals of Mathematic sciences. 

Books 


• Nurettin ERGÜN Kümeler Teorisine Giriş, Ankara 2006. 

Student 







WEEK 

1 Naive set theory, 


2 Logical axioms and inference rules 

3 Axioms of set theory 

4 order pairs 

5 related Functions 

6 equality relations 

7 order relations

8 Order type, 

9 well order sets 


11 partial and completed order sets 

12 order numbers, 

13 finite induction 

14 finite and infinite sets. 

FINAL EXAM



DEPARTMENT OF MATHEMATİC 


Course Title M225 Matrix Algebra I 

Semester: autumn term Language: Turkish 


Instructor 

Dr.Muzaffer Atasoy 

Office Hour 

Email: matasoy@erciyes.edu.tr 

WEB Site: 



Department of mathematic 


Phone: 90 352 4374937 / 33213 

Fax: 90 352 4374933 



Must: 

Elective: yes 

Core: yes Related: Minor: 


Course Content Review of matrix, algebra of square matrices, determinants, method of 

Chio, polynomial of matrices and linear transformations, eigenvalues 

and aigenvectors, quadratic forms and quadratic surfaces, change of 

basis. 


Books • Genel Matematik, M. Balcı, A.Ü. Fen Ed. Fak. Yayınları 

• Calculus, R.A.Adams, Vancouver,Canada , 1994 

• Elementary Linear Algebra, Stanley I. Grassman 

Student 



WEEK 


1 Review of matrix 

2 Review of matrix 

3 Algebra of square matrices 

4 Algebra of square matrices 

5 Determinants 

6 Method of Chio 

7 Polynomial of matrices and linear transformations 


9 Polynomial of matrices and linear transformations 

10 Eigenvalues and aigenvectors 

11 Eigenvalues and aigenvectors

12 Quadratic forms and quadratic surfaces 

13 Quadratic forms and quadratic surfaces 

14 Change of basis. 

FINAL EXAM





Course Title M214 Set Theory II 



Instructor 

Office Hour 

Email: 

WEB: 





Phone: 90 352 4374937 / 

Fax: 90 352 4374933 



Must: 

Elective: Yes 



Course Content Lattices, caunted sets, Number systems, real numbers, epsilon-delta 

methods, proof by induction and other methods of proof. Axiom of 

Choice, Zorn’s Lemma, König’s Lemma., Cardinals, Ordinals, 

Arithmetic of Ordinals and Cardinals numbers, Special Cardinal 

numbers 

Course Objective To understand foundamentals of Mathematic sciences. 

Books 


• Nurettin ERGÜN Kümeler Teorisine Giriş, Ankara 2006. 

• 

Student 







WEEK 

1 Lattices, 


2 caunted sets 

3 Number systems, 

4 real numbers, 

5 epsilon-delta methods,

6 proof by induction and other methods of proof 

7 Axiom of Choice 

8 Zorn’s Lemma 

9 König’s Lemma 


11 Cardinals 

12 ordinals 

13 Arithmetic of Ordinals and Cardinals numbers, 

14 Special Cardinal numbers 

FINAL EXAM



DEPARTMENT OF MATHEMATİC 


Course Title M226 Matrix Algebra II 

Semester: spring term Language: Turkish 


Instructor 

Dr.Muzaffer Atasoy 

Office Hour 

Email: matasoy@erciyes.edu.tr 

WEB Site: 



Department of mathematic 


Phone: 90 352 4374937 / 33213 

Fax: 90 352 4374933 



Must: 

Elective: yes 

Core: yes Related: Minor: 


Course Content Complex quadratic forms, general linear groups, Hermit 

transformation and Hermit matrix, symmetric transformation and 

symmetric matrix,unitary transformation and unitary matrix, 

orthogonal transformation and orthogonal matrix . 


Books • Uygulamalı Lineer Cebir, Ö.Akın,Feryal matbaacılık, 2002 

• Lineer Cebir, E.Esin,H.H.Hacısalihoğlu, E.Özdamar, G.Ü.Fen 

Ed.Fak. Yayını, 1987 

• Elementary Linear Algebra, Stanley I. Grassman, 

Student 



WEEK 


1 Complex quadratic forms 

2 Complex quadratic forms 

3 General linear groups 



6 Hermit transformation and Hermit matrix 

7 Hermit transformation and Hermit matrix 


9 Symmetric transformation and symmetric matrix 

10 Symmetric transformation and symmetric matrix

11 Unitary transformation and unitary matrix 

12 Unitary transformation and unitary matrix 

13 Orthogonal transformation and orthogonal matrix 

14 Orthogonal transformation and orthogonal matrix 

FINAL EXAM





Course Title M237 Metric Spaces I 



Instructor Prof. Dr. Mehmet Baran 

Office Hour 

Email: onem@erciyes.edu.tr WEB: 





Phone: 90 352 4374937 / 33206 

Fax: 90 352 4374933 



Must: 

Elective: Yes 



Yes 

Course Content Definition of metric spaces, examples, open sets, closed sets, closure, 

accumulation points, open spheres in metric spaces, the product of 

metric spaces and submetric spaces, Hölder’s and Minkowski’s 

inequalities, the convergence of sequences, isometri. 


Books • S., Lipshutz, General Topology, Mcgraw-Hill, 1965. 

Student 




1. Hafta metric spaces 

2. Hafta examples 

3. Hafta examples

4. Hafta open sets, closed sets 

5. Hafta accumulation points and interior points 

6. Hafta examples, theorems, 

7. Hafta product spaces, examples, theorems 

8. Hafta Subspaces, examples, theorems 

9. Hafta Hölder and Minkowski Inequalities 

10. Hafta Midterm exam 

11. Hafta Sequences 


13. Hafta isometri 


15. Hafta Final exam





Course Title M238 Metric Spaces II 




Office Hour 






Phone: 90 352 4374937 / 33206 

Fax: 90 352 4374933 



Must: 

Elective: Yes 



Yes 

Course Content To obtain a topology from a metric, equivalent metrics, continuous, 

open, and closed functions, the diameter of a set and bounded set., 

normed spaces, Banach spaces and complete metric spaces. 



Student 




1. Hafta To obtain a topology from a metric and Metrizability 


3. Hafta equivalent metrics

4. Hafta Continuous functions 


6. Hafta open and closed functions 


8. Hafta theorems 

9. Hafta the diameter of a set and bounded set 


11. Hafta normed spaces 


13. Hafta Banach spaces 

14. Hafta complete metric spaces 






Course Title M301 Introduction of Programming I 

Semester: Autumn Term 

Language: Turkish 


Instructor 

Assistant Prof. Dr. M. Tamer ŞENEL 

Office Hour Friday 13-14 

Email: senel@erciyes.edu.tr 

WEB Site: 





Phone: 90 352 4374937 / 33216 

Fax: 90 352 4374933 






Course Content Introduction to computers, Hardware components of a computer: 

CPU, and memory units. Software concepts: System and application 

software.. Windows operating system. Using operating system and 

application. Using word processors, excel and powerpoint softwares. 

Course Objective To teach Students the basic tools of computer, using Packet program 

(Word-Excel-Powerpoint) and application in Mathematics. 

Books • Bilgisayar Kullanımı Yakup Yüksel, Cem Yayınevi, (2000) 

Student 


Students should be attance regularly to lessons and laboraties. (56 

Hours). Also to repeat generally all topics over the exam periods. (20 

hours) (Total 5 ECTS)


WEEK 


1 Basic knowladge. Defination and concepts of computer. 

2 Hardware. 

3 Operation systems-Windows Operation systems 

4 Microsoft word 

5 Openning file and arrange it. 

6 Prepare of Tables. 

7 Mathematical Symbols and application in Mathematics and Word 


9 Microsoft Excel 

10 Basic concepts in Excel 

11 Works in books Excel and cells. 

12 Functions and formulas in Excel 

13 Functions of Mathematical 

14 Graps. 

FINAL EXAM





Course Title M307 Topology I 


Local Credit (T-P-C) : 4-0-4 ECTS Credit: 6 

Instructor Prof Dr. Osman Mucuk 

Office Hour Monday 10-12 

Email: mucuk@erciyes.edu.tr WEB: 





Phone: 90 352 4374937 / 33208 

Fax: 90 352 4374933 






Yes 

Course Content Initial and final topologies, quotient topology, product spaces, infinite 

product spaces, metric product spaces, first countable spaces second 

countable spaces, separable spaces, Lindelöf spaces, separation 

axioms, Urysohn’s Lemma , Tietz extension theorem and metric able 

theorem . 

Course Objective To teach some basic concepts in Topology, to create the ability of 

Mathematical idea and commend, to help to gain the basic topological 

knowledge and ability for their later educations. 

Books • Topology and groupoids, R. Brown, BookSurge LLC, North 

Carolina, 2006. 

• General Topology, Symour LIPSCHUTZ , Schaum’s Outline 

Series, Newyork (1965) 

• Introduction to Metric and Topological Spaces, W. A. 

SSUTHERLAND, Oxford University Press, (1985). 

• Topoloji ve Kategori, O. Mucuk, Nobel Yayınları 2. Baskı 2011 

Student 


Ankara 

To be successful the students have to continue the courses, to repeat 

the topics at home, to do exercises given at the end of topics and to 

repeat generally all topics before taking exam

WEEKLY TOPICS 


1. Week Initial topologies and examples 

2. Week Final topologies and examples 

3. Week Quotient topologies and different examples 

4. Week Finite product spaces 

5. Hafta Infinite product spaces 

6. Week Metric product spaces 

7. Week First countable spaces 

8. Week Second countable and separable spaces 

9. Week Lindelöf spaces 

10. Week Midterm Exam 

11. Week Separation axioms (T0 and T1 spaces) 

12. Week Separation axioms (T2 and T3 spaces) 

13. Week Regüler ve normal spaces 

14. Week Urysohn’s Lemma, Tietz extension theorem and metric able theorem. 

15. Week Final Exam 


Prof. Dr. Osman Mucuk 







Course Title M302 Introduction of Programming II 

Semester: Spring Term 



Instructor 




WEB Site: 





Phone: 90 352 4374937 / 33216 

Fax: 90 352 4374933 






Course Content Algorithmic Approach and Flowcharting, Structure of Fortran 

Language, Elements of Fortran, The Rules of Fortran 

Statements.Loop Structures and Loop ,Fortran Arithmetic Expression, 

Character Expression, Programming Examples. Control Statements 

and Loops, Control Statements ( GO TO Statements Logical 

Statements, If Statements , Logical If ), Aritmetic, Input and Output 

with Arrays, Type and Length Specifications, Type Declaration 

Statements.. Subprograms, Type Subprograms , Character Arrays, The 

Character Statement, The Statement Files in Fortran, Open, Read, 

Write ve Close Statement. 

Course Objective To teach Students rule of programming, and Use Fortran 

Books • Bilgisayar programlama ve Fortran 77, Mustafa Aytaç, H. Kemal 

Sezen, Bete Yayınevi, 6. Baskı (1999) 

• Fortran 77,F. Tokdemir, M.E.T.U. , 1995 

Student 


Students should be attance regularly to lessons and laboraties. (56 

Hours). Also to repeat generally all topics over the exam periods. (20 

hours) (Total 5 ECTS)


WEEK 


1 Algorithmic Approach and Flowcharting 

2 Structure of Fortran Language, Elements of Fortran 

3 The Rules of Fortran Statements. 

4 Fortran Arithmetic Expression, Character Expression 

5 Input and Output (I/O) Statements, Programming Examples. 

6 Control Statements and Loops, Control Statements, GO TO Statements 

7 Logical Statements, If Statements , Logical If, Aritmetic If 

8 Mid-Term Exam 

9 Loop Structures and Loop Expression. The DO Loop Structure, The DO 

Statement in Fortran 

10 Arrays and Subscripted Variables, Subscripted Variables Names, Input and 

Output with Arrays, 

11 Type and Length Specifications, Type Declaration Statements. Programming 

Examples. 

12 Subprograms, Statement Function, Function Type Subprograms 

13 Subroutine Type Subprograms , Programming Examples. 

14 

Character Arrays, The Character Statement, The Arrays Bounds, The 

Character Assignment Statement Files in Fortran, Open, Read, Write ve Close 

Statement 

Final Exam





Course Title M308 Topology II 



Instructor Prof Dr. Osman Mucuk 

Office Hour Monday 10-12 

Email: mucuk@erciyes.edu.tr WEB: 





Phone: 90 352 4374937 / 33208 

Fax: 90 352 4374933 






Yes 

Course Content Compact spaces, sequentially compact spaces, countable compact 

spaces, locally compact spaces, compactifications, connected spaces, 

connected components, locally connected spaces, pats, path connected 

spaces, nets and filters, complete metric spaces and the completeness 

of a metric space, the homotopies of paths, simply connected spaces 

and fundamental groups. 

Course Objective To teach some basic concepts in Topology, to create the ability of 

Mathematical idea and commend, to help to gain the basic topological 

knowledge and ability for their later educations. 

Books • Topology and groupoids, R. Brown, BookSurge LLC, North 

Carolina, 2006. 

• General Topology, Symour LIPSCHUTZ , Schaum’s Outline 

Series, Newyork (1965) 

• Introduction to Metric and Topological Spaces, W. A. 

SSUTHERLAND, Oxford University Press, (1985). 

• Topoloji ve Kategori, O. Mucuk, Nobel Yayınları 2. Baskı 2011 

Student 


Ankara 

To be successful the students have to continue the courses, to repeat 

the topics at home, to do exercises given at the end of topics and to 

repeat generally all topics before taking exam

WEEKLY TOPICS 


1. Week Compact spaces 

2. Week Sequentially compact spaces 

3. Week Countable compact spaces, 

4. Week Local compact spaces and compactification 

5. Hafta Connected spaces 

6. Week Connected components and local connected spaces 

7. Week Paths and path connected spaces 

8. Week Nets and their convergence 

9. Week 

Filters 

10. Week Midterm Exam 

11. Week Complete metric spaces and completion of a metric space 

12. Week Homotopies of paths 

13. Week Simply connected spaces 

14. Week Fundamental groups 

15. Week Final Exam 


Prof. Dr. Osman Mucuk 







Course Title MAT 311 Differential Geometry I 



Instructor 

Yrd.Doç.Dr. Nural YÜKSEL 


Email: yukseln@erciyes.edu.tr 

WEB: 





Phone: 90 352 4374937 / 33215 

Fax: 90 352 4374933 






Course Content Affine Spaces,Euclidean Spaces,Topological Manifolds,Differentiable 

Manifolds,Tangent Vectors and Tangant Spaces,Covariant 

Derivate,Lie Bracket Operation,Cotangent Vectors and Cotangent 

Spaces,1-Forms,Gradient and Divergens Functions,Differential of a 

Map,Submanifolds,Tensörs and Tensör Spaces, External Product 

Spaces. 


Differential geometry. 

Books 

Diferensiyel Geometri,Prof.Dr.H.H.Hacısalihoğlu,İnönü Üniv.Fen- 

Ed.Fak.Yayınları,1983. 

Student 







WEEK 


1 Affine Spaces. 

2 Euclidean Spaces 

3 Topological Manifolds 

4 Differentiable Manifolds 

5 Tangent Vectors and Tangent Spaces

6 Cotangent Vectors and Spaces 

7 Lie Bracket Operation 


9 1-Forms. 

10 Differential of a Map 

11 Sub-Manifolds. 

12 Tensors and Tensor Spaces 

13 Tensors and Tensor Spaces. 

14 External Product Spaces. 

FINAL EXAM





MAT 312 Differential Geometry II 



Instructor 

Yrd. Doç.Dr. Nural YÜKSEL 

Course Title Friday 10.00-12.00 

Semester: Spring Term WEB: 





Phone: 90 352 4374937 / 33215 

Fax: 90 352 4374933 






Course Content The theory of curves, Serret-Frenet vectors, a curve osculating hyper- 

Planes, Curvatures, and the angle between the osculating planes 

Hyper Geometric Meanings of Curvatures, Custom Curves, a curve 

Global Indicators, Surfaces Theory, Riemannian Manifold and 

Covariant Derivative, Gauss' Transformation and Shape Operator, 

Figure Matrix operator of Accounts, Basic Forms and Shape Operator 

algebraic invariants, Euler's Theorem for Hypersurfaces, Olin 

Indicator Rodrigues formulas and Dupin, Gauss' Equations 


Books 

Student 


The aim of this course is to give basic concepts and theorems of 

Differential Geometry. 

Diferensiyel Geometri,Prof.Dr.H.H.Hilmihacısalihoğlu,İnönü 

Üniv.Fen-Ed.Fak.Yayınları,1983. 






WEEK 


1 Introduction to the theory of curves 

2 The Serret-Frenet vectors, 

3 Hyper osculating a curve Planes

4 Curvatures 

5 The angle between the geometric mean veEğriliklerin osculating hyperplanes, 

6 Special Curves. 

7 Global Indicators for a curve 


9 Theory of Surfaces, 

10 Riemannian Manifold and Covariant Derivative 

11 Gauss's Transformation and Shape Operator 

12 Basic Forms and Shape Operator algebraic invariants 

13 Euler's Theorem for Hypersurfaces 

Indicator Olin Rodrigues formulas and Dupin, Gauss's equation 

14 

FINAL EXAM





Course Title M 315 Linear Spaces I 

Semester: Autumm Term Language: Turkish 


Instructor 

Yrd. Doç. Dr. A. Nihal TUNCER 



WEB: 





Phone: 90 352 4374937 / 33218 

Fax: 90 352 4374933 



Must: 

Elective: Yes 




Sets, Functions, Finite Sets, Listing relation, Absolute value, Some 

important inequalities, Real number sequences, continuity, Vector 

spaces, Metric Spaces, Special Metric Spaces, Topological Spaces, 

Normed Spaces 

Course Objective This course gives an information about properties of various sequence 

spaces. 

Books 


• Öner ÇAKAR, Fonksiyonel Analize Giriş, Ankara, 1992. 

• Turgut BAŞKAN, Osman BİZİM, İ. Naci CANGÜL, Metrik Uzaylar 

Ve Genel Topolojiye Giriş, Bursa 2000. 

• Mustafa BAYRAKTAR, Fonksiyonel Analiz, Erzurum 1994. 

• Albert WILANSKY. Functional Analysis, 1964. 

Student 



repeat the topics at home (35 hours), to make homework (5 


generally all topics at the exam periods (29 hours). (Total 5 ECTS 

Credit) 


WEEK 


1 Sets, 

2 Functions, 

3 Finite Sets, Listing relation, 

4 Absolute value, Some important inequalities,

5 Real number sequences, continuity, 

6 Vector spaces, 

7 Metric Spaces, 


9 Special Metric Spaces, 

10 Topological Spaces, 

11 Normed Spaces and Related Theorems, 

12 Metric Subspaces, 

13 Normed Subspaces, 

14 Open and Closed Sets, 

FINAL EXAM





Course Title 

M 316 Linear Spaces II 



Instructor 

Yrd. Doç. Dr. A. Nihal TUNCER 



WEB: 





Phone: 90 352 4374937 / 33218 

Fax: 90 352 4374933 



Must: 

Elective: Yes 



Course Content Convergence and continuity On the Metric and Normed Spaces, Complete and 

Compakt Metric Spaces, Banach Spaces, Linear Spaces, Linear Subspaces, Function 

spaces, Finite and infinite dimensional spaces, Linear Operators. 

Course Objective This course gives an information about properties of various sequence spaces. 

Books 


• Öner ÇAKAR, Fonksiyonel Analize Giriş, Ankara, 1992. 

• Turgut BAŞKAN, Osman BİZİM, İ. Naci CANGÜL, Metrik Uzaylar 

Ve Genel Topolojiye Giriş, Bursa 2000. 



Student Responsibility To be successful the students have to continue to lessons (56 hours), to repeat the 

topics at home (40 hours), to make homework (5 homeworks) given at the end of 

topics (25 hours) and to repeat generally all topics at the exam periods (29 hours). 

(Total 9 ECTS Credit) 


WEEK 


1 Convergence and continuity On the Metric Spaces, 

2 Convergence and continuity On the Normed Spaces, 

3 Complete Metric Spaces, 

4 Compakt Metric Spaces, 

5 Banach Spaces, 

6 Linear Spaces, 

7 Linear Subspaces, 

8 Linear Independence , Linear dependence , 

9 Function Spaces, 


11 Finite and Infinite Dimensional Spaces , 

12 Linear Operators, 

13 Continiuous Linear Operators, Bounded Linear Extensions

14 Linear Functionals and Dual Spaces. 

FINAL EXAM





Course Title M317 Filter Spaces I 



Instructor Yrd. Doç. Dr. Muammer Kula 

Office Hour 

Email: kulam@erciyes.edu.tr WEB: 





Phone: 90 352 4374937 / 33221 

Fax: 90 352 4374933 



Must: 

Elective: Yes 



Yes 

Course Content Topological spaces, neighborhoods, open sets, closed sets, 

accumulation point, subspaces, bases and subbases, continuous, open 

and closed functions, metrics spaces, sequences in metric spaces and 

convergence, finite product spaces and infinite product spaces, the 

separation axioms. 





Student 


WEEKLY COURSE PLAN 

Distribution Session topics will be explained 

1. Week Topological spaces, neighborhoods 

2. Week open sets, closed sets, accumulation point, subspaces

3. Week examples 

4. Week bases and subbases 

5. Week continuous, open and closed functions 

6. Week examples 

7. Week metrics spaces 

8. Week examples, theorems 

9. Week sequences in metric spaces and convergence 

10. Week Midterm exam 

11. Week finite product spaces and infinite product spaces 


the separation axioms 

13. Week 


15. Week Final exam 


Yrd. Doç. Dr. Muammer Kula 







Course Title M318 Filter Spaces II 




Office Hour 






Phone: 90 352 4374937 / 33221 

Fax: 90 352 4374933 



Must: 

Elective: Yes 



Yes 

Course Content Compact spaces, compactness in metric spaces, sequences in 

topological spaces, convergent sequences, examples, nets, subnets, 

filters, filter bases, Comparison of filters and convergence, 

convergence and continuity, ultrafilters, examples, connectedness. 





Student 


WEEKLY COURSE PLAN 

Distribution Session topics will be explained 

1. Week Compact spaces 

2. Week examples

3. Week compactness in metric spaces 


5. Week sequences in topological spaces, convergent sequences 


7. Week nets, subnets 


9. Week filters 


11. Week filter bases 

12. Week Comparison of filters and convergence 

13. Week convergence and continuity, ultrafilters 

14. Week connectedness 










Course Title M 320 Topolojik Gruplar II 



Instructor 

Prof. Osman MUCUK 


Email: mucuk@erciyes.edu.tr 

WEB: 





Phone: 90 352 4374937 / 33208 

Fax: 90 352 4374933 



Must: 

Elective: Yes 



Course Content Connectedness and compactness in topological groups, local compact 

topological groups, covering spaces of topological groups, local 

properties, local homeomorphisms, action of topological groups on 

topological spaces., Lie groups 

Course Objective Although the theory of topological groups was developed mainly in 

order to study groups of Lie types and its impetus came from analysis, 

it soon became useful in purely algebraic concepts. The topological 

group has both topological and algebraic structures, so it is directly 

relevant to both fields of mathematics. The object of this course is to 

teach the student the fundamental concepts of topological groups and 

methods of topological groups. 

Books 

1. P.J. Higgins, Introduction to Topological Groups, Chambridge 

University Press, 1974. 

2. L. Pontrjagin, Topological groups, Princeton University Press,1966. 

3. Topoloji ve Kategori, O. Mucuk, Nobel Yayınları 2. Baskı 2011 

Ankara. 

Student 


Earlier preparation, attending the classes, to repeat the topics at home, 

to make exercises, to repeat the general topics in exam periods 


WEEK 

WEEKLY TOPICS 

1 Connectedness 

2 Connectedness in topological groups 

3 Different exercises 

4 Compactness

5 Compactness in topological groups, 

6 Local compact topological groups, 

7 Covering spaces 


9 Covering groups of topological groups 

10 Universal covering spaces 

11 Construction of a universal covering 

12 Lifting problems in topological groups 

13 Action of topological groups on topological spaces. 

14 Lie groups 

FINAL EXAM





Course Title MAT 319 Topological Groups I 

Semester: Autumn Language: Turkish 


Instructor 

Prof. Osman MUCUK 


Email: mucuk@erciyes.edu.tr 

WEB: 





Phone: 90 352 4374937 / 33208 

Fax: 90 352 4374933 



Must: 

Elective: Yes 



Course Content Algebraic and topological notions, topological groups, subgroups 

and quotient groups of topological groups, product topological 

groups, fundamental systems of neighbourhoods, separation axioms 

in topological groups, homogenous properties 


Although the theory of topological groups was developed mainly in 

order to study groups of Lie types and its impetus came from analysis, 

it soon became useful in purely algebraic concepts. The topological 

group has both topological and algebraic structures, so it is directly 

relevant to both fields of mathematics. The object of this course is to 

teach the student the fundamental concepts of topological groups and 

methods of topological groups. 

Books 1. P.J. Higgins, Introduction to Topological Groups, Cambridge 

University Press, 1974. 

2. L. Pontrjagin, Topological groups, Princeton University 

Press,1966. 

3. Topoloji ve Kategori, O. Mucuk, Nobel Yayınları 2. Baskı 

2011 Ankara 

Student 


Earlier preparation, attending the classes, to repeat the topics at home, 

to make exercises, to repeat the general topics in exam periods 


WEEK 

WEEKLY TOPICS 

1 Algebraic notions 

2 Topological notions,

3 Topological groups and examples 

4 Right and Left translations 

5 Some properties of topological groups 

6 The functions between topological groups 

7 Subgorups and quotient groups of topological groups 


9 Product topological groups, 

10 Fundamental systems of neighbourhoods, 

11 Separation axioms in topological groups 

12 Homogenous properties 

13 İsomorphisms and automorphisms in topological groups 

14 Different exercises 

FINAL EXAM





Course Title M321 Advanced Number theory I 

Semester: Fall Language: Turkish 

Local Credit (T-P-C) : 2 0 2 ECTS Credit:5 

Instructor Yrd. Doç. Dr. Emin AYGÜN 

Office Hour 

Email: eaygun@erciyes.edu.tr WEB: 

Erciyes University, Faculty of Sciences,Department of Mathematics,38039-Kayseri 

/TURKEY Phone: 90 352 4374937 / 33223, Fax: 90 352 4374933 



Must: 

Elective: Yes 



Yes 

Course Content Representation of Integers , Arithmetic Functions, Mobius Functions, 

, Euler’s Q Functions , Dirichlet Product , Multiplicative Functions and 

Dirichlet Inverse, Mangoldt and Lioville Functions, Divisor functions, 

Formal series, Bell series , Derivation on the Arithmetic Functions 

Kriptology 


Books • Introduction to Analytic Number Theory, Tom M. 

Apostol,Springer Verlag, Newyork, 1976 

• Sayılar Teorisi ve Uygulamaları, H. ALTINDIS, Kayseri, Turkey, 

1999 

Student 


Course Outline 

1st week Representation of Integers, 

2nd week Arithmetic Functions 

3rd week Mobius Functions 

4th week Euler’s Q Functions.

5th week 

6th week 

7th week 

8th week 

9th week 

10th 

week 

11th 

week 

12th 

week 

13th 

week 

14th 

week 

Dirichlet Product 

Multiplicative Functions and Dirichlet Inverse 

Mangoldt and Lioville Functions 

Midterm exam 

Lioville Functions 

Divisor functions 

Formal series, Bell series 

Derivation on the Arithmetic Functions 

Bell series 

Kriptology 

Final exams 


Yrd. Doç. Dr. Emin AYGÜN 

Öneren Anabilim Dalı Başkanı





Course Title 

Mat.322 Advanced Number Theory II 


Local Credit (T-P-C) 2 0 2 ECTS Credit: 5 

Instructor 

Yrd. Doç. Dr. Emin AYGÜN 

Office Hour Friday : 14.00_ 16.00 

Email: 

WEB Site: 

altindis@erciyes.edu.tr 





Phone: 90 352 4374937 / 33205………. 

Fax: 90 352 4374933 



Must: Yes Related: Minor: 


Course Content Representations of integers, Computer operations with 

integers,Applications of Congruences,Recurrence Functions, 

Continued Fractions, Cryptology. 


Books 

Elementary Number Theory and ıt’s Applications, Kenneth 

H.Rosen,Addison Wesley, Newyork, 1988. 

Student 

To be successful the students have to continue to lessons (28 hours),. 



WEEK 


1 Computer operations with integers 

2 Divisibility tests 

3 The Perpetual calendar 

4 Magic Squares for odd n 

5 Magic squares for n divisible by 4. 

6 Recurrence Functions 

7 Continued Fractions, 

8 ARA SINAV 

9 Periodic continued fractions 

10 Quadratic Irrational 

11 Applications of Continued fractions 

12 Introduction to Cryptology 

13 Chracter and Block Ciphers

14 Exponentiation Ciphers. 

YARIYIL SONU SINAVI





Course Title M323 Mathematical Programming I 

Semester: Autumn 



Instructor 




WEB Site: 





Phone: 90 352 4374937 / 33216 

Fax: 90 352 4374933 



Must: 

Elective: Evet 



Course Content Maple, Matlab, Matcad 

Course Objective To teach the use of mathematical programs. 

Books 1-Basri Çelik, Maple ve Maple ile Matematik, 2009. 

2- Ahmet Altınbaş, Matlab, Değişim Yayınları, 2006. 

Student 

Students should be attance regularly to lessons and laboraties. (28Hours). Also to 

Responsibility repeat generally all topics over the exam periods. (10 hours) (Total 66 hours/25 = 3 

ECTS) 


WEEK 

1 Introduction to Matlab 

Install Matlab 

2 


3 

4 

5 

Menu 

Commands 

Functions

6 

7 

8 

9 

10 

11 

12 

13 

14 

Functions 

Matrix 

Midterm Exam 

Solution of Equations 

Solution of Differential Equations 


Graph 

Graph 

Graph





Course Title M324 Mathematical Programming II 

Semester: Spring 



Instructor 




WEB Site: 





Phone: 90 352 4374937 / 33216 

Fax: 90 352 4374933 



Must: 

Elective: Yes 



Course Content Maple, Matlab, Matcad 

Course Objective To teach the use of mathematical programs. 

Books 1-Basri Çelik, Maple ve Maple ile Matematik, 2009. 

2- Ahmet Altınbaş, Matlab, Değişim Yayınları, 2006. 

Student 

Students should be attance regularly to lessons and laboraties. (28Hours). Also to 

Responsibility repeat generally all topics over the exam periods. (10 hours) (Total 66 hours/25 = 3 

ECTS) 


WEEK 

1 Introduction to Maple 

Install Maple 

2 


3 

4 

5 

Menu 

Commands , Functions 

Matrix

6 

7 

8 

9 

10 

11 

12 

13 

14 

Solution of Equations 


Midterm Exam 

Graph 

Introduction to Matcad 

Menu 

Functions 

Functions 

Graph





Course Title M331 Differential Equations I 



Instructor Prof. Dr. Fuat GÜRCAN 

Office Hour 

Email: gurcan@erciyes.edu.tr WEB: 





Phone: 90 352 4374937 / 33221 

Fax: 90 352 4374933 






Yes 

Course Content An Introduction to Differential Equations; The Differential Equation 

of a Family of Curves; Existence and Uniqueness Theorems for IVP, 

Substitution Techniques, Exact and Linear Equations, The Equations 

of Bernoulli and Ricatti; The Ordinary and Singular Points of a First- 

Order Equation, The Clairaut Equation; Approximate Solutions 

(Direction Fields, Picard’s Methods), Applications of First-Order 

Differential Equations 

Course Objective The aim of this course is to help the student graps the nature and 

significance of differential equations and to provide a wealth of 

examples and problems in the physical sciences. 

Books • A First Course in Differential Equations, Dennis G. Zill, Inc., 

Boston, 1973. 

• Ordinary Differential Equations, Morris Tenenbaum and 

Herry Pollard, New York: Harper& Row, 1963,1985 

• Elementery Differential Equations with Applications, William 

R. Derrick, Stanley I. Grossman, University of Montana, 

Student 


Addison-wesley Pubishing Company, 1976 




all exam periods. (10 hours)



1. Hafta Definition of Differential Equations; First-Order Differential Equations, The 

Differential Equation of a Family of Curves 

2. Hafta Existence and Uniqueness Theorems for IVP 

3. Hafta Substitution Techniques (Homogeneous Equations and Reducable to the 

Homogeneous Equation) 

4. Hafta Exact Equations, 

5. Hafta Techniques of integrating factors 

6. Hafta Linear Equations and an simple application of Linear Equations 

7. Hafta The Equations of Bernoulli and Ricatti 

8. Hafta The Ordinary and Singular Points of a First-Order Equation, 

9. Hafta The Clairaut Equation and Envelopes 


11. Hafta General Substitution Techniques 

12. Hafta Approximate Solutions(Direction Fields and Picard’s Methods), 

13. Hafta 

Applications of First-Order 

Trajectories) 

Linear Differential Equations (Orthogonal 

14. Hafta Applications of First-Order Non-Linear Differential Equations (Curves of 

Pursuit) 






Course Title M332 Differential Equations II 




Office Hour 






Phone: 90 352 4374937 / 33221 

Fax: 90 352 4374933 






Yes 

Course Content Linear Higher-Order Differential Equations; Existence and 

Uniqueness Theorems for IVP and BVP, Solutions of Linear 

Equations, Constructing a Second Solution From a Known Solution, 

Homogeneous Linear Equations with Constant Coefficients, 

Undetermmined Coefficient, Variation of Parameters, Differential 

Equations with variable Coefficients, Power Series Solutions, The 

Laplace Transform 

Course Objective The aim of this course is to help the student graps the nature and 

significance of differential equations and to provide a wealth of 

examples and problems in the physical sciences. 

Books • A First Course in Differential Equations, Dennis G. Zill, Inc., 

Boston, 1973. 

• Ordinary Differential Equations, Morris Tenenbaum and 

Herry Pollard, New York: Harper& Row, 1963,1985 

• Elementery Differential Equations with Applications, William 

R. Derrick, Stanley I. Grossman, University of Montana, 

Student 


Addison-wesley Pubishing Company, 1976 




all exam periods. (10 hours)



1. Hafta Linear Higher-Order Differential Equations; Preliminary Theory 

2. Hafta Existence and Uniqueness Theorems for IVP and BVP, 

3. Hafta Linear Dependence and Linear Independence, Solutions of Linear Equations, 

4. Hafta Constructing a Second Solution From a Known Solution, Homogeneous Linear 

Equations with Constant Coefficients, 

5. Hafta Undetermmined Coefficient, The operator Methods 

6. Hafta Variation of Parameters 

7. Hafta Differential Equations with variable Coefficients, Special Methods 

8. Hafta The Cauchy-Euler Equation 

9. Hafta Power Series Solutions, Solutions Around Ordinary Points 


11. Hafta Solutions Around Singular Points 

12. Hafta Two Special Equations 

13. Hafta 

The Laplace Transform, The Inverse Transform 

14. Hafta Operational Properties, Applications 






Course Title M333 Numerical Analaysis I 




Office Hour 






Phone: 90 352 4374937 / 33221 

Fax: 90 352 4374933 



Must: 

Elective: Yes 



Yes 

Course Content Review of Calculus, The Solution Of Nonlinear Equations F(x)=0, 

The Solution Of Nonlinear Systems 

Course Objective The aim of this course is to help the student graps the theory and 

applications of numerical analysis and their solutions in the physical 

sciences. 

Books 

1- Mathews, JH ;Numerical methods for Mathematics, Science and 

engineering, Printice-Hall Inc. A Simon &Schuster Company, US, 

1992. 

2- Hildebrand, FB ; Introduction to Numrical analysis (second 

edition), McGraw-Hill, New York, 1974 

3- Kreyszic, E ; Advanced engineering mathematics, John Wiley and 

Sons, Inc., 1993 (seventh edition). WJF ;Numerical Methods for 

Bifurcations of Dynamical Equilibria, SIAM,2000. 

Student 








1. Hafta Review of Calculus 

2. Hafta Binary Numbers and Error Analysis

3. Hafta Bisection Methods 

4. Hafta Regula Falsi and Newton Methods 

5. Hafta Fixed-Point Iteration Method 

6. Hafta Rate of Convergence 

7. Hafta Acceleration of Convergence 

8. Hafta The solution of Linear Systems, General Theory 

9. Hafta Gausssian Elimination 


11. Hafta Machine Implementation, Pivoting Strategies 

12. Hafta Non-Linear Systems, Introduction 

Method of Steepest Descent 

13. Hafta 

14. Hafta Newton’s Method for Systems, Applied Problems 






Course Title M334 Numerical Analaysis II 




Office Hour 






Phone: 90 352 4374937 / 33221 

Fax: 90 352 4374933 



Must: 

Elective: Yes 



Yes 

Course Content Polynomial Interpolation, Approximation of Functions, Numerical 

differentiation and Integration 

Course Objective The aim of this course is to help the student graps the theory and 

applications of numerical analysis and their solutions in the physical 

sciences. 

Books 

1- Mathews, JH ;Numerical methods for Mathematics, Science and 

engineering, Printice-Hall Inc. A Simon &Schuster Company, US, 

1992. 

2- Hildebrand, FB ; Introduction to Numrical analysis (second 

edition), McGraw-Hill, New York, 1974 

3- Kreyszic, E ; Advanced engineering mathematics, John Wiley and 

Sons, Inc., 1993 (seventh edition). WJF ;Numerical Methods for 

Bifurcations of Dynamical Equilibria, SIAM,2000. 

Student 






Course Outline 

1. Hafta Basic Princibles and Theory 

2. Hafta The Lagrange Polynomial

3. Hafta The Newton Divided Difference Form 

4. Hafta The Newton Forward Difference Formula 

5. Hafta The Aitken Interpolation Algorithm 

6. Hafta Error Terms and Error Estimation 

7. Hafta Splines 

8. Hafta Taylor Polynomials, Chebyesehev Polynomial Approximations 

9. Hafta Least Squares Approximations 


11. Hafta Numerical Differentiation Formulas, Some Error Analysis 

12. Hafta Richardson Extrapolation 

Numerical Integration Formulas 

13. Hafta 

14. Hafta Simpson and Trapezoit Composite Formulas 






Course Title M336 Dynamical Systems II 

Semester: Spring Language: Turkish 


Instructor Asist. Prof. Dr. Ali Deliceoğlu 

Office Hour Friday 15:00-17:00 

Email: adelice@erciyes.edu.tr WEB: 





Phone: 90 352 4374937 / 33221 

Fax: 90 352 4374933 



Must: 

Elective: Yes 

Core Related:Yes Minor 


Yes 

Course Content Bifurcation theory; saddle-node bifurcation, transcritical bifurcation, 

pitchfork bifurcation, hopf bifurcation. Chaos 

Course Objective The aim of this course is to help how to solve a nonlinear equations by 

using dynamical systems with applications to biology, physics, etc. 

Books • Nonlinear Dynamics and Chaos, Steven H. Strogatz, Perseus 

Books Publishing , 1994. 

• Introduction to applied nonlinear dynamical systems and chaos, S. 

Wiggins, Springer-Verlag, New York, 1990. 

• Differential Equations: A Dynamical Systems Approach, J. H. and 

Student 


B. H. West, Springer-Verlag, 1990. 


repeat the topics at home (20 hours) to make homework (10 


generally all topics all exam periods. (40 hours) 



1. Hafta Bifurcation theory

2. Hafta Saddle-node bifurcation, transcritical bifurcation, pitchfork bifurcation 

3. Hafta Hopf bifurcation 

4. Hafta Global bifurcations of circles 

5. Hafta Poincare maps 

6. Hafta Normal form 

7. Hafta Chaos 

8. Hafta Lorenz equations 

9. Hafta Strange attractor 


11. Hafta Logistic maps: Numerics and analitical 

12. Hafta Fractals 

13. Hafta Countable and uncountable sets 

14. Hafta Box dimensional 

15. Hafta Final exam 


Asist. Prof. Dr. Ali Deliceoğlu 







Course Title M335 Dynamical Systems I 



Instructor Asist. Prof. Dr. Ali Deliceoğlu 

Office Hour Friday 15:00-17:00 

Email: adelice@erciyes.edu.tr WEB: 





Phone: 90 352 4374937 / 33221 

Fax: 90 352 4374933 



Must: 

Elective: Yes 

Core Related:Yes Minor 


Yes 

Course Content Introduction to dynamical systems; choas, fractals and dynamics, a 

dynamical view of the world and the importance of being nonlinear. 

One-dimensional flows; flows on the line, flows on the circle 

Course Objective The aim of this course is to help how to solve a nonlinear equations by 

using dynamical systems with applications to biology, physics, etc. 

Books • Nonlinear Dynamics and Chaos, Steven H. Strogatz, Perseus 

Books Publishing , 1994. 

• Introduction to applied nonlinear dynamical systems and 

chaos, S. Wiggins, Springer-Verlag, New York, 1990. 

• Differential Equations: A Dynamical Systems Approach, J. H. 

Student 


and B. H. West, Springer-Verlag, 1990. 


repeat the topics at home (20 hours) to make homework (10 


generally all topics all exam periods. (40 hours) 


Anlatılacak Konuların Dönemlik Dağılımı

1. Hafta Introduction to dynamical systems 

2. Hafta Choas, fractals and dynamics 

3. Hafta A dynamcis wies of the world and the importance of being nonlinear 

4. Hafta One-dimensional flows 

5. Hafta Flows on the line 

6. Hafta Bifurcation theory 

7. Hafta Flows on the circle 

8. Hafta Two-dimensional flows 

9. Hafta Linear systems 


11. Hafta Phase diagrams 

12. Hafta Limits cycles 

13. Hafta Poincare Bemdixson theorem 

14. Hafta Conservative and reversible systems 



Asist. Prof. Dr. Ali Deliceoğlu 







Course Title M 337 Applied Mathematics I 



Instructor 

Asist. Prof. Pakize TEMTEK 


Email: temtek@erciyes.edu.tr 

WEB: 





Phone: 90 352 4374937 / 33214 

Fax: 



Must: Elective: Yes 

Core : Yes Related: Minor 


Course Content Improper integrals, The Laplace Transform; definition, existence and 

basic properties of the Laplace Transform, the inverse transform and 

the convolution, Laplace Transform solution of linear differential 

equations with constant coefficients, Laplace Transform solution of 

constant coefficient linear systems. 

Course Objective The objective of this course is to teach the student theoretical and 

practical aspects of Laplace transform. 

Books 

Following boks are recommended. 

• Uygulamalı Matematik, Yaşar İ. B.,GaziÜni. No: 127, (1988). 

• Laplace Dönüşümleri, Murray R., Schaum’s Outline Series, Mc 

Graw-Hill Book Company. 

• Element of Pure and Applied Math., Mc Lass, Graw-Hill Book 

Company. 

Student 





generally all topics all exam periods. (6 hours) (Total 5 ECTS)


WEEK 


1 Improper integrals and applications 

2 Laplace Transformation of some elementary functions 

3 Piecewise continuous functions 

4 Exponential order functions 

5 Existence of the Laplace transform 

6 Basic properties of the Laplace transform 

7 General applications 


9 The inverse transform 

10 Basic properties of the inverse transform 

11 The convolution 

Laplace transform solution of linear differential equations with constant 

12 

coefficients 

13 Laplace transform solution of linear systems with constant coefficients 


FINAL EXAM





Course Title M 338 Applied Mathematics I I 



Instructor 




WEB: 





Phone: 90 352 4374937 / 33214 

Fax: 



Must: Elective: Yes 

Core : Yes Related: Minor 


Course Content Gamma and Beta Functions, Fourier Series, Convergence of Fourier 

Series, Theorems on Fourier series, Fourier Cosine Series, Fourier 

Sine Series, the integration of Fourier series, Parseval’s formula. 


practical aspects of Fourier series. 

Books 

Following boks are recommended. 

• Fourier Analizi, Yarasa R.,İst.Devlet Müh.ve Mim.Akademisi 

Yayınları,No:131(1976) 

• Fizik ve Mühendislikte Matematik Yöntemler, B. Karaoğlu, Bilgi 

Tek Yayıncılık,(1997) 

• Uygulamalı Matematik, Yaşar İ. B.,GaziÜni. No: 127, (1988). 

• Element of Pure and Applied Math., Mc Lass, Graw-Hill Book 

Company. 

Student 







WEEK 


1 Special functions: Factorial functions, Gamma and Beta functions 

2 Periodic functions 

3 Definition of Fourier Series and Dirichlet condition 

4 Convergence of Fourier Series 

5 Theorems on Fourier series 

6 Fourier series of functions with 2L and 2π period 



9 Fourier cosine series, Fourier sine series 

10 Dirichlet integration formula, Parseval’s formula. 

11 The integration and derivative of Fourier series 

12 The complex form of the Fourier series 

13 Fourier series of two variables functions 

14 General examples 

FINAL EXAM





Course Title M 339 Theory of Divergent Series I 

Semester: : Fall Smester Language: Turkish 


Instructor Asist.Prof. Abdulcabbar SÖNMEZ 

Office Hour Friday:10:00-11:00 






Phone: 90 352 4374937 / 33217 

Fax: 90 352 4374933 



Must: 

Elective: Yes 



Yes 

Course Content Basic set theory, Metric and semimetric spaces, Complete metric 

spaces, Inequalities, Principle of Uniform boundedness, Sequence 

spaces , Linear operators and funtionals, Norm of Bounded linear 

operators, The Banach –Steinhaus theorems and applications. 

Course Objective The aim of the course is to give basic concepts that are necessray for 

the thorough perception of summability and sequence spaces. 

Books 

Aşağıdaki kitaplar tavsiye edilir. 

• G. H. Hardy, Divergent series, Oxford University Press, (1949). 

• R.E. Powell and S.M. Shah, Summability theory and 

applications, New Delhi, (1988). 

• I.J.Maddox, Elements of Functional Analaysis,Cambrıdge at 

the University Press 1970 

Student 




repeat generally all topics at the exam periods . 


WEEK 

CHAPTER TOPICS

1 Basic set theory and analysis 

2 Metric and semimetric spaces, Complete metric spaces. 

3 Category and uniform boundedness 

4 Inequalities, 

5 Abel Limit Theorem 

6 Sequence spaces and applications 

7 semicontinious functions. 

8 Principle of Uniform boundedness 

9 Linear metris spaces and basis. 


11 Paranorms,seminorms and norms 

12 Linear operators and funtionals 

13 Norm of Bounded linear operators 

14 The Banach –Steinhaus theorems and applications. 

15 FINAL EXAM. 









Course Title M 340 Divergent Series Theory II 


Local Credit (T-P-C) : 2 0 2 ECTS Credit:5 

Instructor Asist.Prof.Abdulcabbar SÖNMEZ 







Phone: 90 352 4374937 / 33217 

Fax: 90 352 4374933 



Must: 

Elective: Yes 



Yes 

Course Content Abel and Cesaro convergence, Nörlund , Riesz ,Holder,Euler and 

Housdorff means,Abel’s Inequality, Matrix transformations in 

sequence spaces, Sequence to sequence , Series to sequence and 

Series to series transformations, Kojima- Schur Theorems, Tauberian 

Theorems based upon the Cesaro and Abel Methods. 

Course Objective Dizi uzaylarında matris dönüşümleri detaylı olarak en iyi şekilde 

öğretilir. Bazı yüksek lisans derslerinin temelleri burada atılır. 

Books 

Aşağıdaki kitaplar tavsiye edilir. 

• G. H. Hardy, Divergent series, Oxford University Press, (1949). 

• R.E. Powell and S.M. Shah, Summability theory and 

applications, New Delhi, (1988). 

• I.J.Maddox, Elements of Functional Analaysis,Cambrıdge at 

the University Press 1970 

• 

Student 






WEEK 

TOPICS 

1 Abel and Cesaro convergence and related to theorems, 

2 

Holder,Euler and Housdorff means and related to theorems 

3 

4 

5 

6 

Abel’s Inequality 

Euler-Maclaurin Sum Formula 

Matrix transformations in sequence spaces 

The Silverman-Toeplitz Theorems 

7 Sequence to sequence transformations and related to theorems 

8 

9 

Series to sequence transformations and related to theorems 

Series to series transformations and related to theorems 


11 Kojima- Schur Theorems 

12 Schur theorem, 

13 Tauberian Theorems based upon the Cesaro and Abel Methods 

14 Nörlund ve Riesz means 

15 FINAL EXAM 









Course Title M 341 Advanced Calculus I 

Semester: Autumm Term Language: Turkish 


Instructor 

Dr. A. Nihal TUNCER 



WEB: 





Phone: 90 352 4374937 / 33218 

Fax: 90 352 4374933 



Must: 

Elective: Yes 



Course Content Improper integrals, types of integral and convergence criterions, beta 

and gamma functions. 


Books 

Student 


Special functions which is oftenly used in mathematics and physics 

will be introduced. 


• Saffet Süray, İleri Analiz, Ankara, 1978. 

• Earl D. Rainville, Special Functions. Macmillan, 1960. 

• Ian N. Sneddon, Special Functions of Mathematical Physics and 

Chemistry. Oliver and Boyd, 1956 






WEEK 

1 Definition of improper integrals 

2 Types of improper integral 

3 1. Type of improper integrals, 

4 1. Type of improper special integrals, 

CHAPTER TOPICS

5 Convergence criterions for 1. Type of improper integrals, 

6 Absolute and conditional Convergence for 1. Type of improper integrals, 

7 2. Type of improper integrals, 

8 2. Type of improper special integrals, 

9 Convergence criterions for 2. Type of improper integrals, 


11 3. Type of improper integral, 

12 Regülar convergence of improper integrals, 

13 Gamma functions and its applications 

14 Beta functions and its applications 

FINAL EXAM




Course Title 


M351 Transformations and Geometries I 


Local Credit (T-P-C) : 3 13.5 ECTS Credit: 3.5 

Instructor Yrd. Doç. Dr. Nural Yüksel 


Email: yukseln@erciyes.edu.tr WEB: 





Phone: 90 352 4374937 / 33215 

Fax: 90 352 4374933 



Must: 

Elective: Yes 


Elementary: Intermediate: 

Yes 

Advanced: Specialized: 



Recalling the life issues of education will be useful to students of 

geometry, and the future is to prepare teacher 

Books • Ramazan Şahin, ÖSS ye Hazırlık ,Zambak Yayınları, Geometri 1 

• Ramazan Şahin, ÖSS ye Hazırlık ,Zambak Yayınları, Geometri 2 

Student 




Cartesian Coordinates 

1. Hafta 

Cartesian graph drawings 

2. Hafta

3. Hafta 

4. Hafta 

5. Hafta 

6. Hafta 

7. Hafta 

8. Hafta 

9. Hafta 

10. Hafta 

11. Hafta 

12. Hafta 

13. Hafta 

14. Hafta 

15. Hafta 

Polar Coordinates 

Graphic drawings in Polar Coordinates 

Angle Types 

The triangle and the elements 

The concept of Polygon 

MID-TERM EXAM 

Triangle types 

Triangle angles and angle relationships 

Angle-side triangle relations 

Solving problems 

Co-triangles 

Theorems associated with triangles 

FINAL EXAM 


Yrd. Doç. Dr. Nural Yüksel 







Course Title M 342 Advanced Calculus II 



Instructor 

Dr. A. Nihal TUNCER 



WEB: 





Phone: 90 352 4374937 / 33218 

Fax: 90 352 4374933 



Must: 

Elective: Yes 



Course Content Fourier series, Fejer theorem, Theorems of convergence, Orthogonal 

functions. 

Course Objective Special functions which is oftenly used in mathematics and physics 

will be introduced. 

Books 

Student 



• Saffet Süray, İleri Analiz, Ankara, 1978. 

• Earl D. Rainville, Special Functions. Macmillan, 1960. 

• Ian N. Sneddon, Special Functions of Mathematical Physics and 

Chemistry. Oliver and Boyd, 1956 






WEEK 

1 Periodic functions, 


2 Fourier series, 

3 Conditions of Dirichlet 

4 Odd and even functions, 

5 Parseval identity

6 Differential and integral of Fourier series, 

7 Complex notations of Fourier series, 

8 Orthogonal functions, 

9 Quasi region Fourier series, 


11 Convergence of Fourier series, 

12 Fourier integrals, 

13 Parseval identity for Fourier integrals, 

14 Elliptical integrals and functions. 

FINAL EXAM





Course Title M352 Transformations and Geometries II 


Local Credit (T-P-C) : 3 013,5 ECTS Credit: 3.5 

Instructor Yrd. Doç. Dr. Nural Yüksel 

Office Hour 

Email: yukseln@erciyes.edu.tr WEB: 





Phone: 90 352 4374937 / 33215 

Fax: 90 352 4374933 



Must: 

Elective: Yes 



Yes 



Recalling the life issues of education will be useful to students of 

geometry, and the future is to prepare teacher 

Books • Ramazan Şahin, ÖSS ye Hazırlık ,Zambak Yayınları, Geometri 1 

• Ramazan Şahin, ÖSS ye Hazırlık ,Zambak Yayınları, Geometri 2 

Student 



Session topics will be explained Distribution 

The concept of similar triangles 

1. Week 

Similar triangles and the basic axiom of proportionality theorem 

2. Week

3. Week 

4. Week 

Theorems of similar triangles 

Theorems of Tales, Menelaus and Seva 

5. Week 

6. Week 

7. Week 

Similarity theorems related to the results 

Vertical similar triangles 

Upright triangles metric relations 


Pythagorean theorem and its consequences 

9. Week 

General examples 

10. Week 

Quadrilaterals and Public Facilities 

11. Week 

Special quadrangles: trapezoidal, parallelogram and rhombus 

12. Week 

Special rectangles: a rectangular, square, deltoid 

13. Week 

Solving problems 

14. Week 



Yrd. Doç. Dr. Nural Yüksel 







Course Title M415 Category Theory I 


Local Credit (T-P-C) : 3 13.5 ECTS Credit: 9 


Office Hour 






Phone: 90 352 4374937 / 33221 

Fax: 90 352 4374933 



Must: 

Elective: Yes 



Yes 

Course Content Definition of category and examples, Sections, retractions, 

isomorphisms, monomorphisms, epimorphisms and bimorphisms, 

initial, final and zero objects, products and coproducts, equalizers, 

functors and properties, Composition of functors and natural 

transformations, natural isomorphisms. 


Books • G. Preuss, Foundations of Topology, Kluwer Academik 


• Herrlıch, H. and Strecker E. G., Category Theory, Allyn and 

Bacon Inc., Boston, 1973. 

• Adamek J., Herrlıch, H. and Strecker E. G., Abstract and 

Concrete Categories, A Wiley- Interscience Publication John 

Wiley & Sons, Inc., New York, 1990. 

Student 

Responsibility



1. Hafta Definition of category and examples 


3. Hafta Sections, retractions, isomorphisms, monomorphisms, epimorphisms and 

bimorphisms 


5. Hafta initial, final and zero objects 


7. Hafta products and coproducts 


9. Hafta equalizers 


11. Hafta functors and properties 


13. Hafta 

Composition of functors and natural transformations, natural isomorphisms. 











Course Title M416 Category Theory II 


Local Credit (T-P-C) : 3 013,5 ECTS Credit: 9 


Office Hour 






Phone: 90 352 4374937 / 33221 

Fax: 90 352 4374933 



Must: 

Elective: Yes 



Yes 


Pullbacks and pushouts diagrams, limits, colimits, stacks and filters, 

stack convergence space and filter convergence space, filtered 

categories and filtered colimits, setvalued functors, E-reflective 

subcategories, factorization structures for functors, Topological 

Categories and examples. 




• Herrlıch, H. and Strecker E. G., Category Theory, Allyn and 

Bacon Inc., Boston, 1973. 

• Adamek J., Herrlıch, H. and Strecker E. G., Abstract and 

Concrete Categories, A Wiley- Interscience Publication John 

Wiley & Sons, Inc., New York, 1990. 

Student 

Responsibility



1. Hafta Pullbacks and pushouts diagrams 

2. Hafta Examples, theorems 

3. Hafta limits, colimits 


5. Hafta stacks and filters, stack convergence space and filter convergence space 


7. Hafta filtered categories and filtered colimits, setvalued functors setvalued functors 


9. Hafta E-reflective subcategories 


11. Hafta factorization structures for functors 


13. Hafta 

Topological Categories and examples. 











Course Title M 421 Abstract Algebra I 


Local Credit (T-P-C) : 3 1 3,5 ECTS Credit: 9 

Instructor 




WEB: 





Phone: 90 352 4374937 / 33210 

Fax: 90 352 4374933 



Must: 

Elective: Yes 

Core Related: Yes Minor 


Course Content Groups and subgroups, Cosets, Cyclic groups, Symmetric groups, 

Group homomorphisms, Normal subgroups, Quotient groups, Direct 

products, Semi-direct products, Direct sums, Free groups, The Sylow 

theorems, Nilpotent and solvable groups. 

Course Objective This course gives an advanced treatise on group theory in order to 

prepare the student for more advanced topics in abstract algebra such 

as ring and field theory given at 4 th spring term. 

Books 


Student 


1. E. BAYAR, Soyut Cebir, Karadeniz Teknik Üniversitesi, Fen- 

Edebiyat Fakültesi Yayını, Trabzon, 1986. 

2. F. ÇALLIALP, Çözümlü Soyut Cebir Problemleri, İTÜ, Fen- 

Edebiyat Fakültesi Yayını, İstanbul, 1995. 

3. Y. CHOW, Modern Abstract Algebra, Gordon and Breach 

Science Publishers Inc., New York, 1976. 






generally all topics at the exam periods (20 hours). (Total 9 ECTS) 

Weekly Schedule

WEEK 


1 Groups. 

2 Subgroups. 

3 Cosets and conjugate elements. 

4 Cyclic groups. 

5 Symmetric groups. 

6 Group homomorphisms. 

7 Normal subgroups and isomorphism theorems. 


9 Quotient groups. 

10 Direct products, semi-direct products and direct sums. 

11 Free groups, generators and relations. 

12 The action of a group on a set. 

13 The Sylow theorems. 

14 Nilpotent and solvable groups. 

FINAL EXAM





Course Title M 422 Abstract Algebra II 



Instructor 




WEB: 





Phone: 90 352 4374937 / 33210 

Fax: 90 352 4374933 



Must: 

Elective: Yes 

Core Related: Yes Minor 


Course Content Rings, Integral domains, Fields, Ring homomorphisms, Quotient 

rings, Ideals, Factorization domains and unique factorization domains, 

Polynomials, Modules, Algebras. 

Course Objective The objective of the course is to provide the students with the 

knowledge about ring and field theory. Students must have a 

background on group theory. 

Books 


Student 


1. E. BAYAR, Soyut Cebir, Karadeniz Teknik Üniversitesi, Fen- 

Edebiyat Fakültesi Yayını, Trabzon, 1986. 

2. F. ÇALLIALP, Çözümlü Soyut Cebir Problemleri, İTÜ, Fen- 

Edebiyat Fakültesi Yayını, İstanbul, 1995. 

3. Y. CHOW, Modern Abstract Algebra, Gordon and Breach 

Science Publishers Inc., New York, 1976. 






generally all topics at the exam periods (20 hours). (Total 100 

hours/25 = 4 ECTS)


WEEK 


1 Rings, 

2 Integral domains. 

3 Division rings and fields. 

4 Ring homomorphisms. 

5 Ideals. 

6 Quotient rings. 

7 Maximal and prime ideals. 


9 Principal ideals and principal ideal domains. 

10 Isomorphism theorems. 

11 Unique factorization domains. 

12 Polynomials. 

13 Modules. 

14 Algebras. 

FINAL EXAM





Course Title M432 Partial Differential Equations II 



Instructor 




WEB: 





Phone: 90 352 4374937 / 33214 

Fax: 0 352 4374933 






Course Content Classification of second order partial differential equations, eliptic 

differential equations, Cauchy Problem, Adjoint Differential Operator, 

Laplace Equation and applications, Poisson Equation, Dirichlet’s 

Principle and harmonic function, the one and two-dimensional wave 

differential equations and boundary value problems. 


practical aspects of partial differential equations. 

Books • Prasad P. and Ravindran R.; Partial Differential Equations , Wiley 

Easter Limited, 1991 (Second Ed.) 

• Haberman, R.; Elementary Applied Partial Differential Equations 

with Fourier Series and Boundary Value problems, Prentice-hall, 

Inc. New Jersey, 1983. 

• Kreyszic, E ; Advanced engineering mathematics, John Wiley and 

Sons, Inc., 1993 (seventh edition).Following books are 

recommended. 

• Aliyev G.G.; Kısmi Türevli Diferansiyel Denklemler, M.E.B., 

Student 


İstanbul,1995. 






WEEK 


1 Classification of almost-linear second order partial differential equations 

2 The normal (or canonical) form 

3 The Cauchy Problem 

4 Adjoint operator, Green’s formula, Self-adjoint differential operator 

5 Elliptic differential equations, Dirichlet and Neumann Problem 

6 Basic defination and theories for harmonic functions 

7 Separation of variables in Laplace’sequation and Poisson’s integral formula 


9 Solution of Laplace’s equations in polar coordinate 

10 Dirichlet problem for circle 

11 Heat equation and boundary value problems 

12 Initial value problem for one dimentional homogeneous wave equations 

13 Solutions for one dimentional wave equations by using separation variables 

Initial and bounded value problem for the wave equations and solutions of the wave 

14 

equations in polar coordinate 

FINAL EXAM





Course Title M431 Partial Differential Equations I 



Instructor 




WEB: 





Phone: 90 352 4374937 / 33214 

Fax: 0 352 4374933 






Course Content Partial Differential Equations of a Family of Surfaces, Classification, 

First Order Linear and Quasi-Linear Differential Equations, Cauchy 

Problem, First Order Non-Linear Differential Equations, Method of 

Charpit, Solution of a Characteristic Cauchy Problem, Complete 

Integral, First Order in more than two independent Variables. 


practical aspects of partial differential equations. 

Books • Partial Differential Equations , Prasad P and Ravindran R ; Wiley 

Easter Limited,(Second Ed.) 1991. 

• Elementtary Applied Partial Dfferential equations with Fourier 

Series and Boundary Value problems, Haberman, R., Prenticehall, 

Inc. New Jersey, 1983. 

• Kısmi Türevli Dif. Denk., Aliyev G. G., M.E.B.,2001. 

Student 


• Kısmi Türevli Denk., Koca K., A.Ü.F.F. No:33,1995. 






WEEK 


Basic concepts related with partial diff. equ. and classification of equations. 

1 

Formation of equations. 

2 Relation between surface families (normal, tangent,..)in partial diff. equ. 

3 First order linear partial differential equations 

4 First order quasi-linear equations. Method of Lagrange. 

5 Generalization of method of Lagrange and introduction of Cauchy Problem. 

6 Existence and uniqueness theorems for Cauchy Problem and application. 

7 First order non-linear partial differential equations. 


9 Method of Lagrange-Charpit. 

10 Special types of non-linear first order equation, Clairaut’s equation. 

11 Singular solutions for non-linear first order equations and envelope. 

Linear second order partial differential equations with constant coefficients, 

12 

operator form and separation method. 

13 Repeat again separation of operator and exp. solutions. 

The Euler equation and special methods of solving the non-homogeneous 

14 

equations. 

FINAL EXAM





Course Title M 439 Theory of Complex Functions I 



Instructor Asist.Prof. Abdulcabbar SÖNMEZ 







Phone: 90 352 4374937 / 33217 

Fax: 90 352 4374933 



Must: 

Elective: Yes 



Yes 

Course Content The Field of Complex Numbers , Analytic Functions, The 

Complex Exponential, The Cauchy-Riemann Theorem,Harmonic 

functions, Contour Integrals,Functions and sequnce on the Field 

of Complex Numbers, Antiderivatives, Cauchy’s Theorem, 

Cauchy’s Integral Formula, Cauchy’s Theorem for Chains 

Course Objective The aim of the course is to teach fundemental concepts and their 

applications on the field of complex numbers . 


1)Joseph BAK,Donald J.Newman, Complex Analysis, Second 

Edition,Springer-Verlag 1996 

2) Watson Fulk;Complex Variables An Introductions,Marcel 

Dekker,,Inc.Newyork.Hong Kong,1993. 

3) Prof.Dr.Ali DÖNMEZ, Karmaşık Fonksiyonlar Kuramı, 

İstanbul,Ağustos 1999. 

Student 






WEEK 


1 The Field of Complex Numbers and Polar coordinates 

Functions and sequnce on the Field of Complex Numbers and their 

2 applications 

3 ,Analytic Functions and their applications 

4 The Complex Exponential, trigonometric, hyperbolic and logharithmic functions 

5 ,The Cauchy-Riemann Theorem and their applications. 

Harmonic functions and their applications 

6 

7 Contour Integrals and their applications. 

8 Antiderivative and exercices 

9 Cauchy’s Theorem and their applications 

10 MIDTERM EXAM. 

11 Morera ve Liouville Theorems and Their applications 

12 

13 

14 

Cauchy’s Integral Formula and their applications. 

Cauchy’s Integral Formula for derivatives and their applications 

Cauchy’s Theorem for Chains and their applications 

15 FINAL EXAM. 









Course Title M 440 Theory of Complexs Functions II 










Phone: 90 352 4374937 / 33217 

Fax: 90 352 4374933 



Must: 

Elective: Yes 



Yes 

Course Content Representation with the series of Analytic function, Power seris and 

radius, Taylor series Uniform convergence, Isolated sıngularities and 

Laurent series, Resıdue Theory,Evaluation of definite integral,Infinite 

products, Analytic continuation 

Course Objective The aim of this course is to enhance the students’ awareness of field of 

complex numbers and notions related to it. 


1)Joseph BAK,Donald J.Newman, Complex Analysis, Second 

Edition,Springer-Verlag 1996 

2) Watson Fulk;Complex Variables An Introductions,Marcel 

Dekker,,Inc.Newyork.Hong Kong,1993. 

3) Prof.Dr.Ali DÖNMEZ, Karmaşık Fonksiyonlar Kuramı, 

İstanbul,Ağustos 1999. 

Student 






WEEK 


1 Series representation of Analytic function 

2 

Convergent of sequence and series , Uniform convergence Weirstrass-M 

criteria. 

3 Power and Taylor series and their applications . 

4 Isolated sıngularities and Laurent series and their applications 

5 Inroduction to resıdue theory 

6 Application of Laurent series and finding the residue 

7 Cauchy’s Residue Theorem and ıts application. 

8 Contour Integral Tekniği yardımıyla Belirli integral hesabı. 

9 Evaluation of definite integral 


11 Calculation of definite integral by means of residues 

12 Integral applications 

13 Infinite products and applications 

14 Analytic continuation and applications 

15 FINAL EXAM 









Course Title M 449 Real Analysis 



Instructor 




WEB: 





Phone: 90 352 4374937 / 33209 

Fax: 90 352 4374933 



Must: 

Elective: Yes 



Course Content Set Theory, Measure , Outer Measure ,Lebesque Outer 

Measure,Measurable Sets,Integration of Simple Functions,Integration 

of Positive Functions ,Integrable Functions, Lebesque Integral, 

L p Space , L 

∞ 

Space 

Course Objective Aim of this course is to teach real number system and to give 

concepts that are basic to other courses such as calculus, functional 

analysis, differential equations etc. 

Books 


• Mustafa Balcı, Reel Analiz , Ankara Üniversitesi Fen Fakültesi 

yayınları, (1998). 

• H. L. Royden, Real Analysis, (1963). 

Student 






WEEK 


1 Set Theory 

2 Classes of Some Sets 

3 Measure and related theorems 

4 Examples on measure 

5 Outer measure and related theorems 

6 Examples on outer measure 

7 Lebesque outer measure 

8 Lebesque measure 

9 Measurable functions and their applications 


11 Integration of simple functions 

12 Integration of positive functions and related theorems 

13 Integrable functions and related theorems 

14 Relation between Lebesque and Reimann integral 

FINAL EXAM





Course Title M 450 Functional Analysis 



Instructor 




WEB: 





Phone: 90 352 4374937 / 33209 

Fax: 90 352 4374933 



Must: 

Elective: Yes 



Course Content Metric Spaces, Inequalities, Topological Spaces, Linear Spaces, 

Normed Spaces, Banach Spaces, Finite and infinite dimensional 

spaces, Function spaces,Quotient spaces,Linear 

Operators,Fundemental theorems about normed spaces, Open 

mappings, closed graph theorem.,Hilbert Spaces ,Banach algebras 

Course Objective To meet the students with the concept of abstract spaces and with the 

related theorems. 

To help them acquire the ability of analyzing such spaces and notions 

defined on them. 

Books 

Student 




• Tosun TERZİOĞLU, Fonksiyonel Analizin Yöntemleri, İstanbul, 

1998. 






WEEK 


1 Metric Spaces and related theorems 

2 Examples counter-examples of Metric spaces 

3 Open and closed sets 

4 Topological spaces 

5 Complete spaces 

6 Linear spaces 

7 Norm and related theorems 

8 Inequalities 

9 Banach Spaces 


11 Function spaces 

12 Finite and infinite dimensional spaces 

13 Linear transformations 

14 Linear functionals 

FINAL EXAM





Course Title M451 Convergent Spaces I 


Local Credit (T-P-C) : 3 13.5 ECTS Credit: 9 


Office Hour 






Phone: 90 352 4374937 / 33206 

Fax: 90 352 4374933 



Must: 

Elective: Yes 



Yes 

Course Content Definition of stacks and filters, examples, (constant) stack convergence 

spaces, (constant) filter convergence spaces, (constant) local filter 

convergence spaces, the products, qoutient and subspaces of these 

convergent spaces, separation properties in these convergent spaces. 




Student 




1. Hafta Definition of stacks and filters, examples

2. Hafta (constant) stack convergence spaces 

3. Hafta (constant) filter convergence spaces 

4. Hafta (constant) local filter convergence spaces 



7. Hafta qoutient spaces, examples, theorems 

8. Hafta Subspaces, examples, theorems 

9. Hafta T0 and T1 convergence spaces 


11. Hafta T2 convergence spaces 






Prof. Dr. Mehmet Baran 







Course Title M452 Convergent Spaces II 


Local Credit (T-P-C) : 3 13,5 ECTS Credit: 3.5 


Office Hour 






Phone: 90 352 4374937 / 33206 

Fax: 90 352 4374933 



Must: 

Elective: Yes 



Yes 

Course Content Limit convergence spaces, Uniform spaces, pre-uniform spaces, semiuniform 

spaces, quasi-uniform spaces. The products, qoutient and 

subspaces of these convergent spaces, separation properties in these 

convergent spaces. 




Student 




1. Hafta Limit convergence spaces


3. Hafta Uniform spaces 


5. Hafta pre-uniform spaces 


7. Hafta semi-uniform spaces 


9. Hafta quasi-uniform spaces 



12. Hafta qoutient spaces, examples, theorems 





Prof. Dr. Mehmet Baran 







Course Title M 453 PROBABILITY AND STATISTICS I 



Instructor 

Prof. Dr. İlhan Öztürk 

Office Hour Thursday: 10.00-12.00 

Email: ozturki@erciyes.edu.tr 

WEB: 





Phone: 90 352 4374937 / 33228 

Fax: 90 352 4374933 



Must: 

Elective: Yes 



Course Content Basic Concepts,Data Analysis, Measures of Central Tendency, 

Measures of Dispertion, Probabılıty, 

Course Objective The goal of this course is to show the students commenting basic 

statistics and probability conceppts and aplications. 

Books 


Student 


1.Probability & Statistics for Engineers &; Scientists, Ronald E. 

Walpole at al, Pearson Education LTD.,2007. 

2.Essential of Statistics,David Brink, Ventus Publishing,2010. 

3. Lecture Notes statıstıcs and probabılıty,Robert J. Boik.2004. 

4.Olasılık ve İstatistik, Fikri Akdeniz. 





Weekly Schedule

WEEK 


1 Fundamental Conceps, of Statistics 

2 Data Analysis- The Frequency Distribution Tables 

3 Data Analysis- The Frequency Distribution Tables. 

4 Measures of Central Tendency 

5 Measures of Central Tendency 

6 Measures of Dispertion 

7 Measures of Dispertion 

8 Probability-İntroductıon- Sample points and Counting Techniques 


10 Probability Axioms- 

11 Coditional . Probability 

12 Bayes’ Rule 

13 Bayes’ Rule and Applications 

14 Examples and applications 

FINAL EXAM 









Course Title M 454 PROBABILITY AND STATISTICS II 



Instructor 


Office Hour Thursday: 10.00-12.00 

Email: ozturki@erciyes.edu.tr 

WEB: 





Phone: 90 352 4374937 / 33228 

Fax: 90 352 4374933 



Must: 

Elective: Yes 



Course Content Random Variables and Probability Distributions, Mathematical 

Expectation, Some Discrete Probability Distributions, Some 

Continuous Probability Distributions 

Course Objective The goal of this course is to show the students commenting basic 

statistics and probability conceppts and aplications. 

Books 


References 

1.Probability & Statistics for Engineers &; Scientists, Ronald E. 

Walpole at al, Pearson Education LTD.,2007. 

2.Essential of Statistics,David Brink, Ventus Publishing,2010. 

3. Lecture Notes statıstıcs and probabılıty,Robert J. Boik.2004. 

4.Olasılık ve İstatistik, Fikri Akdeniz. 

Student 






Weekly Schedule

WEEK 


1 Random Variables and Probability Distributions 

2 Random Variables and Probability Distributions 

3 Mathematical Expectation and their propertys 

4 Mathematical Expectation and their propertys 

5 Variances and its propertys 

6 Mean and Variances of Linear Combinations of Random Variables 

7 Mean and Variances of Linear Combinations of Random Variables 

8 Examples 


10 Some Discrete Probability Distributions. 

11 Some Discrete Probability Distributions 

12 Some Continuous Probability Distributions. 

13 Some Continuous Probability Distributions. 

14 Examples and applications. 

FINAL EXAM

ERCIYES UNIVERSITY - Fen FakÃ¼ltesi - Erciyes Ãniversitesi

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