Reasoning and Proof in Mathematics

MHF 3202

Spring 2026

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Time:  MWF period 

Place:   207 Little Hall

Email:  avince@ufl.edu 

Office :  438 Little Hall

Office hours: MWF period 4 or by appointment

Textbook:  Proof and the Art of Mathematics by J. D. Hamkins

Course Description

A main goal is to prepare prospective mathematics majors for courses in which obtaining and proving mathematical statements is essential.  To quote George Polya fon solving a problem:

“If it challengses your curiousity and brings into play your invention, faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery.” 

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Suggested Weekly Problems

See canvas.

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Topics 

Deductive reasoning

Mathematical Induction

Four basic steps:  (1) Understanding the problem, (2) devising a plan, (3) carrying out the plan, (3) looking back

Heuristicss

Examples from the following subjects:

     Number theory

     Discrete Mathematics

     Geometry

     Graph Theory

     Real Analysis

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Grades

Three exams, each worth a third of the final grade.

     Exam 1.   February 9

     Exam 2.   March 13

     Exam 3.   April 20

The exams will be graded on a sliding scale, the harder the exam, the more lenient the grading.  Out of 100, it will never be stricter than 90A, 80B, 70C, 60D.

Weekly problems will be suggested, but not graded.

At most 5 unexcused absences.  More than this will result in a reduction of one letter grade (A->B, B->C, C->D, D->F) in the course.

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Campus Resources

       This course complies with all UF academic policies. For information on those polices and for resources for students, please see this link.

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