P.K. BRODHEAD - Indian River State College

P.K. BRODHEAD
IRSC, Math Dept., 3209 Virginia Ave., Fort Pierce, FL 34981 • +1 724 954 1212 • pbrodhea@irsc.edu • http://faculty.irsc.edu/faculty/pbrodhead/
EDUCATION
Ph.D., Mathematics, University of Florida
Thesis: Computable Aspects of Closed Sets; Advisor: Douglas Cenzer
M.S., Mathematics, University of Florida
B.S., Mathematics, University of Wisconsin- Madison
EMPLOYMENT
Assistant Professor, Indian River State College
Assistant Professor, Virginia State University
Assistant Professor, University of Hawaii at Manoa
Lecturer, University of Hawaii at Manoa
Research Assistant, Victoria University of Wellington (New Zealand; Grant-funded)
Research Assistant, Chinese Academy of Sciences (Beijing; NSF Grant)
Teaching/Research Assistant, University of Florida
Graduate Assistant, University of the Virgin Islands
RESEARCH INTERESTS
Computatabilty, Algorithmic Randomness, Applications of Logic, Computational Complexity,
Effective Mathematics, Unsolvability and Applications, Foundations of Mathematics
PUBLICATIONS
• Journal Articles
1. Algorithmic Randomness and Capacity of Closed Sets, with Douglas Cenzer,
Ferit Toska, and Sebastian Wyman, Logical Methods in Computer Science, Vol.
6 (2011) 1–16.
2. Algorithmic Randomness of Continuous Functions, with G. Barmpalias, D.
Cenzer, J.B. Remmel, and R. Weber, Archive for Mathematical Logic 45
(2008) 533–546.
3. Effectively Closed Sets and Enumerations, with D. Cenzer, Archive for
Mathematical Logic 45 (2008) 565–582.
4. Continuity of Capping in CbT, with A. Li, and W. Li, Annals of Pure and
Applied Logic 155 (2008) 1–15.
5. Algorithmic Randomness of Closed Sets, with G. Barmpalias, D. Cenzer, S.
Dashti, and R. Weber, J. of Logic and Computation 17 (2007) 1041–1062.
• Conference Proceedings, Refereed
1. Bounded Randomness, with R. Downey, and K. M. Ng, Workshop on Theo-
-retical Computer Science 2012 (Calude Festschrift), M.J. Dinneen et al. (Eds.),
Lecture Notes in Comp. Sci. 7160, Springer, Heidelberg (2012) 59–70.
2. Effective Capacity and Randomness of Closed Sets, with D. Cenzer, Proceed-
-ings: Computability and Complexity in Analysis 2010, and Electronic Notes
in Theoretical Computer Science 24 (2010) 67–76.
3. The Strength of the Grätzer-Schmidt Theorem, with B. Kjos-Hanssen,
Proceedings: Computability in Europe 2009, Ambos-Spies, Löwe, and
Merkle (Eds.), Lecture Notes in Computer Science 5635 (2009) 59–67.
4. Numberings and randomness, with B. Kjos-Hanssen, Proceedings:
Computability in Europe 2009, Ambos-Spies, Löwe, and Merkle (Eds.),
Lecture Notes in Computer Science 5635 (2009) 49–58.
5. Random Continuous Functions, with D. Cenzer and J. Remmel, Pro-
1
2008
2005
2000
8/10 –
8/09 – 8/10
8/08 – 7/09
1/08 – 5/08
8/07 – 12/07
6/07 – 7/07
6/03 – 5/07
6/06
2011
2008
2008
2008
2007
2012
2010
2009
2009
2007

ceedings: Third Int. Conf. on Computability and Complexity in Analysis
(2006) 76–89, and Electronic Notes in Th. Comp. Sci. 167 (2007) 275–287.
0
6. Enumerations of Π 1 Classes: Acceptability and Decidable Classes, Pro-
-ceedings: Third Int. Conf. on Comput. and Complexity in Analysis (2006),
and Electronic Notes in Theoretical Computer Science 167 (2007) 289–301
7. Random Closed Sets, with D. Cenzer and S. Dashti, Proceedings: Comput.
in Europe 2006, Beckmann, Berger, Loewe, and J.Tucker (Eds.): Log. Appr.
to Computational Barriers, Lecture Notes in Comp. Sci. 3988 (2006) 55–64.
• Technical Reports, Unpublished
1. Primary Decomposition of Ideals Arising from Hankel Matrices, with M.
Cummings & C. Seidler, SIMU Undergraduate Research (2000) 19–34.
TEACHING EXPERIENCE (F/S/J denote Fall/Spring/Summer)
61 Classes, Fall 2004-Fall 2012
• MAS 4203 - Number Theory (1 time): S11
• MAS 3105 - Applied Linear Algebra (1 time): F11
• STA 2023 - Statistics I (3 times): F12, S11 (2x)
• MAC 2313 - Calculus III (3 times): J12, J11, S09
• MAC 2312 - Calculus II with computer lab using Maxima (1 time): S09
• MAC 2311 - Calculus I with computer lab using Derive (2 times): F08, S08
• MAC 2311 - Calculus I Honors (1 time): F10
• MAC 2311 - Calculus I (4 times): F11, F10, S05 (2x)
• MAC 2233 - Business Calculus I (7 times): F12, J12, S10, F09 (2x), S08, F08
• MAC 1147 - Precalculus Algebra and Trigonometry (2 times): F04 (2x)
• MAC 1140 - Precalculus Algebra via Interactive TV with Tablet PC (1 time): F11
• MAC 1114 - Trigonometry (1 time): S10
• MAC 1105 - College Algebra (10 times): F12 (2x), F11, F10 (3x), S10 (2x), F09 (2x)
• MGF 2106 - Math for Liberal Arts I (3 times): S12 (3x)
• MAT 1033 - Intermediate Algebra (11 times): F12-3x, S12-3x, F&J11, S11-2x, F10
Research Experiences For Undergraduates (REU)
• University of the Virgin Islands, funded by Southeast AGEP, Summer 2006
Topics: Matlab, Linear Algebra, Fourier Analysis, Medical Imaging
Technology – Used in the Classroom
• Learning Software: MathXL, Hawkes, WebAssign, WileyPlus
• Computing Software: Matlab, Maxima, Derive, Excel, TI-84, TI-nspire, Maple,
Singular, Macaulay2
• Communication Methods: Tablet PC, Fluidmath, Elluminate, ANGEL, Blackboard
- Tablet PC Lectures are uploaded to ANGEL, in PDF format, immediately following class
AWARDS & GRANTS
• Travel Grants, for Research Conferences (Various Sources; Competitive)
IRSC Faculty (2010-2012), VA State Univ. Faculty (2010); Univ. FL College of
Liberal Arts and Sciences (2008); Univ. FL Center for Applied Mathematics
(2007, 2008); Univ. FL Graduate Student Council (2007, 2008); SEAGEP
(2006, 2007); Association for Symbolic Logic (2005, 2006, 2007)
• University of Florida
SEAGEP Fellowship (2006-2008); International Research Award (2007);
Alumni Fellowship (2003-2007); FL Board of Education Fellowship (2003)
• National Science Foundation
NSF Grant # 0714151 (EAPSI Fellowship), as Principle Investigator
2
2007
2006
2000
Year
2011
2011
2011-12
2009, 11-12
2009
2008
2010
2005, 10-11
2008-10
2004
2011
2010
2009-12
2012
2010-12
2006
2005-2012
2003-2008
2007

• Summer Institute in Mathematics, University of Puerto Rico
NSF Research Experience for Undergraduates (Participant)
• University of Wisconsin-Madison
Frank D. Cady Math Scholarship (2000); VIGRE Grant (1999-2000); Ronald
E. Mcnair Scholarship (1998-2000); Chancellor’s Scholarship (1997-2000);
U.S. Naval ROTC Scholarship (1997-1998)
COLLABORATION
• RESEARCH WORKSHOPS
1. Buenos Aires Semester in Computability, Complexity, and Randomness
2. Wolfram Technology Conference, Champaign, IL
3. Winter 2012 MidAtlantic Mathematical Logic Seminar, FL Atlantic Univ.
4. Reverse Mathematics: Foundations and Applications, Univ. of Chicago
5. Florida Summer School in Algorithmic Randomness, Univ. of Florida
6. Computability and Complexity Workshop, Univ. of Auckland, New Zealand
7. Effective Randomness Workshop, American Instit. of Math., Palo Alto, CA
• TEACHING DEVELOPMENT
1. National Council of Teachers of Math. Annual Meeting, Indianapolis, IN
2. International Conference on Techn. in Collegiate Mathematics, Denver, CO
3. Math Major Development Meeting, University of Central Florida, Orlando, FL
• ADVOCACY OF THE PROFESSION
1. AFC 63rd Annual Convention, Palm Harbor, FL
2. AFC Region V Fall Conference, Fort Lauderdale, FL
3. AFC Joint Commissions Spring Conference, Tallahassee, FL
4. AFC Region V Spring Conference, Fort Lauderdale, FL
5. AFC 62nd Annual Convention, Naples, FL
6. AFC Membership Development Conference, Sarasota, FL
7. AFC Joint Commissions Spring Conference, St. Augustine, FL
• Co-organized Equity Commission presentations, with Adrienne Jefferson
8. AAUP Advocacy Workshop, Assembly of State Conferences, Deland, FL
LECTURES
• CONFERENCE LECTURES
1. Computability and Complexity in Analysis, Zhenjiang, China
Effective Capacity and Randomness of Closed Sets
2. Conference on Logic, Computability, & Randomness, South Bend, IN
Effective Capacity and Random Closed Sets
3. 16
3
th Southeastern Logic Symposium, Gainesville, FL
Recent Results in Random Closed Sets
4. 116 th Annual Meeting of the Am. Math. Society, San Francisco, CA
The Strength of the Grätzer-Schmidt Theorem
5. AMS Fall Eastern Sectional Meeting, Middletown, CT
Random Reals and Numberings of Computable Trees
6. Joint AMS-New Zealand Math. Soc. Meeting, Wellington, New Zealand
Continuity of Capping in CbT,
7. Annual Graduate Student Conference in Logic, Chicago, IL
The Theory of Numberings and Effectively Closed Sets
8. New York Graduate Student Logic Conference, New York, NY
Enumerations of Families of Effectively Closed Sets
9. Association for Symbolic Logic Annual Meeting, Gainesville, FL
Effectively Closed Sets and Enumerations
2000
1997-2000
Spring 2013
Oct 2012
Jan 2012
Nov 2009
Jun 2008
Dec 2007
Aug 2006
April 2011
Mar 2011
Feb 2011
Oct 2012
Aug 2012
May 2012
April 2012
Oct 2011
July 2011
May 2011
April 2011
June 2010
May 2010
Feb 2010
Jan 2010
Oct 2008
Dec 2007
Apr 2007
Mar 2007
Mar 2007

10. Conference on Logic, Computability, & Randomness, Buenos Aires, Arg.
Random Sets and Functions
11. Computability and Complexity in Analysis, Gainesville, FL
Enumerations of Effectively Closed Sets
12. AMS Fall Eastern Sectional Meeting, Storrs, CT
Algorithmic Randomness of Closed Sets and Continuous Functions
13. SACNAS Annual Meeting, Tampa, FL
Random Closed Sets II [Received: Honorable Mention Award.]
14. Greater Boston Logic Conference, Boston, MA
Random Closed Sets
15. Annual Graduate Student Conference in Logic, Madison, WI
Decidable Π 0
1 Classes: Indices for Leafless Trees aren’t Guaranteed
16. SACNAS Annual Meeting, Denver, CO
Computable Permutations of Π 0
1 Classes
• INVITED RESEARCH LECTURES (AT OUTSIDE INSTITUTIONS)
17. Indiana University of Pennsylvania, Indiana, PA
Algorithmic Complexity and Randomness, Colloquium Talk
18. Florida Altantic University (Honors College), Jupiter, FL
Alg. Complexity & Undecidability: Exs. & Applications, Colloquium Talk
19. Norfolk State University, Norfolk, VA
Algorithmic Randomness, Colloquium Talk
20. Nova Southeastern University, Fort Lauderdale, FL
Algorithmic Randomness, Colloquium Talk
21. West Virginia University, Morgantown, WV
Random Sets and Functions, Colloquium Talk
22. University of Hawaii at Manoa, Honolulu, HI, (given while at Univ. FL)
Enumerations of Solution Sets given by Effect. Closed Sets, Logic Seminar
23. University of Auckland, Auckland, New Zealand
Effective Capacity and Random Closed Sets, Workshop Talk
• OTHER LECTURES (NON-SEMINAR)
24. University of Florida, Gainesville, FL (Service Talk)
International Funding Opportunities, SEAGEP Lecture Series
25. University of Wisconsin-Madison, Madison, WI (Undergraduate Math Talk)
Hilbert’s 10 th Problem, Undergraduate Math Project, Fall 1999.
SERVICE – MATHEMATICS COMMUNITY
• PANELS AND COMMITTEES
1. Referee, Journal of Symbolic Logic
2. NSF panel member
3. Organizing Committee, Florida Summer School in Algorithmic Randomness
4. Organizer, Computability Seminar, University of Florida
5. Organizing Committee, SEALS Annual Meetings
6. Organizing Committee, CCA Annual Meeting
• MENTORING PROGRAMS (UNDERREPRESENTED POPULATIONS)
1. Undergraduates: Math. REU, Univ. of the Virgin Islands
2. Graduate Students: Florida Board of Education, University of Florida
3. High School Students: Summer Science Institute, University of Wisconsin
Jan 2007
Nov 2006
Oct 2006
Oct 2006
May 2006
Apr 2006
Oct 2005
May 2010
Jan 2010
May 2009
Mar 2009
Mar 2009
Apr 2008
Dec 2007
Mar 2008
May 2000
2008
2005-2007
2004-2006
2006
Summer 2006
Summer 2004
Summer 1999
• PROFESSIONAL MEMBERSHIPS
• Research: American Mathematical Society (AMS), Association for Symbolic Logic (ASL)
Computability and Complexity in Analysis (CCA), Computability in Europe (CIE)
• Teaching: National Council of Teachers of Mathematics (NCTM), American Mathematical
4

Association of Two-Year Colleges (AMATYC), Florida Two-year College Mathematics
Association (FTYCMA)
• Profession: American Association of University Professors (AAUP), American Association
of University Women (AAUW), Association for Women in Mathematics (AWM),
Association of Florida Colleges (AFC) – Commission Membership: Faculty, Equity,
Instructional Innovation
• RECOGNITIONS
• Who’s Who: in America (2008), in Science and Engineering (2011-2012)
SERVICE – INDIAN RIVER STATE COLLEGE (FALL 2010-PRESENT)
• TRANS-DISCIPLINARY ENTREPRENEURSHIP INITIATIVE, PAPERS:
• Looking Toward the Future: Alternative Careers and Opportunities for Advancement
with Alexis Neeson, Alfred Williams, and Marta Cronin, Fall 2010.
• Careers and Number Theory with Relevancy to Math Education Majors,
implemented in Number Theory, Spring 2011.
• COLLEGE COMMITTEE WORK
• Honors Committee, Academic Years 2010-11, 2011-12
- Helped to develop and organize the College Honors Program
• Brain Bowl Committee, Academic Years 2010-11, 2011-12
- Helped organize and service this yearly statewide student cross-disciplinary competition
• Planning and Assessment Committee, Spring 2011, & Academic Year 2011-12
- Charged with developing and implementing metrics for assessment and continuing
improvement in all areas college-wide, in preparation for SACS Accreditation
- Studied and developed reviews of best practices:
• Article Review: 2011-2112 Education Criteria for Performance Excellence
• Article Review: The Gradebook Project
- Collaborated with Broward and Brevard Colleges, at the General Education Outcomes
and Assessments Seminar, Broward College, February 9, 2012.
• Great Explorations, Faculty Subcommittee, Fall 2011
- Logistical contributions in weekly meetings. The daylong Great Explorations IRSC
Career Showcase is for high school students in the local five-county region.
- Contributed Career Overview submissions for the Division of Arts and Sciences
• DEPARTMENTAL INVOLVEMENT
• College Problem of the Month Competition, Spring 2011, developed & ran the program
• Curriculum Instructional Guidelines (joint work), Fall 2011
• Event Organization/Participation: Calculus Workgroup (Spring 2012), AMATYC National
Exam (Each semester), Math Olympics (Each spring), Brain Bowl Regional Tournament
(Feb 2011), 50
5
th Anniversary Showcase (Fall 2010)
• Organized: Texas Instruments TI-Nspire Software Seminar, Math Department, Aug 19, 2011
• ASSOCIATION OF FLORIDA COLLEGES (AFC), IRSC CHAPTER
• 2011, President-Elect and Contributing board member
- Participation: Jeans & Jersey Tailgate, Chili Cook-off, Carnation Sale, Golf Tournament
- Additional Contributions: Digitized 2004 and 2009 scrapbooks, June 2011 Luncheon
• 2012, Chapter President, with 26 board members, See: afcirsc.wordpress.com
- Responsibilities: Fundraisers for Student Scholarships, Monthly Board Meetings,
Monthly Educational Luncheons across all 5 campus sites, Community Service Drives,
Social Events for Chapter Members, Membership Drives, Political Activities that raise
awareness of the state legislative agenda, State Commission participation (for all 17 state
commissions), Publication of Chapter activity in the media, Chapter Reports to the State
Office, An ongoing Chapter Scrapbook, Notifications of Awards and Competitions.