Mathematics 314 (was 241)
Foundations of Mathematics (3)
http://www.utm.edu/~caldwell/classes/314/
 
[ Prerequisites | Catalog Description | Goal | Objectives | Text | Outline | Grading | Homework | Old Tests ]
Teacher:
 Dr. Caldwell, office 429 Holt Humanities, phone 7336.  Department office 7360. Email: caldwell@utm.edu.
Prerequisites:
 Mathematics 140 or equivalent.
Catalog Description:
 Proof techniques, sets, propositional calculus, functions, relations, properties of integers.

Teacher's note:  This is our "introduction to proof" course and is a prerequisite to most of the upper division mathematics courses.  The concept of "proof" is fundamental to the culture of mathematics.

Students who plan to graduate in four years should take this class in (or before) the fall semester of their sophomore year.  This is especially important for Secondary Education majors.
Grade:
   25%   tests (about 4 one-hour tests) 
  52%   homework (proofs assigned daily) 
  20%   final (comprehensive) 
    3%   participation (classroom board work and discussion)
Attendance:
 Attendance is mandatory and is enforced via the participation grade.
Homework:
 Homework will be collected every day at the beginning of the class period--have it ready. No late homework accepted.
Goal:
 To prepare students for success in upper division proof-based mathematics courses by familiarizing students with the basic notations, definitions, and proof styles of mathematics. 
Objective:
 The student will: 
  1. Read and understand proofs and recognize invalid proofs. 
  2. Construct and present proofs using a variety of proof techniques including: direct proofs, proofs by contradiction, proofs by mathematical induction. 
  3. Understand and apply the terminology, notation, and concepts associated with each of the following areas: 
    • the algebra of sets 
    • propositional calculus (including quantifiers) 
    • relations (especially equivalence and recurrence relations) 
    • the algebra of functions (especially in/sur/bi-jections) 
    • properties of the integers (including division algorithm, gcd, prime factorization) 
Text:
 Proofs and Fundamentals--a First Course in Abstract Mathematics, Ethan D. Bloch, Birkhäuser Boston, 2000, ISBN: 0-8176-4111-4.
Outline:
 To be determined, one possibility follows.
chapter
topic
days

1
2
3
4
5
6
*

Informal Logic (1-5)
Strategies for Proofs (1-6)
Sets (1-3)
Functions (1-5)
Relations (1-3)
Infinite and Finite Sets (1-4)
Topics from Chapters 7 on

6
8
4
6
4
5
3
  One Hour Tests 4
  40