MATH 622 Selected Topics in Modern Algebra I

f. Normal Subgroupsg. LaGrange's TheoremV. Homomorphism and Factor Groupsa. Homomorphismb. Isomorphism and Cayley's Theoremc. Factor Groupsd. Factor-Group Computations and Simple Groupse. Groups in GeometryVI. Introduction to Ringsa. Definition and Examplesb. Integral domains, subringsc. Fieldsd. IsomorphismVII. The Familiar Number Systemsa. Ordered Integral Domainsb. The Integersc. Field of Quotientsd. Field of Rational Numberse. Ordered Fieldsf. Field of Real Numbersg. Complex Roots of Unity5. Evaluation Measures for Determining Students’ Grades1. Tests and Quizzes 50%2. Homework assignments and projects 15%3. Final exam 35%Note: Individual instructors may weigh evaluation measures differently.6. BibliographyA. Required TextFraleigh, John B. A First Course in Abstract Algebra, 5 th ed., Reading, MA, Addison-Wesley, 1994.Note: In mathematics courses it is usually preferable to have a designated textbookwhich helps to focus the discussion and standardize the language and symbolism.B. Additional Required ReadingsNoneC. Supporting BibliographyArtin, M. Algebra, Englewood Cliffs, NJ, Prentice-Hall, 1991.