Mathematics
Foundations of Mathematics (3)
http://www.utm.edu/~caldwell/classes/241/

Note: This course was renumbered Math 314 starting Fall Semester 2007

[ Prerequisites | Catalog Description | Goal | Objectives | Text | Outline | Grading | Assignments | 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.  Students who plan to graduate in four years should take it 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) 
  50%   homework (proofs assigned daily) 
  20%   final (comprehensive) 
    5%   participation (classroom board work and discussion)
Attendance:
 Attendance is mandatory and is enforced via the participation grade.
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:
 Foundations of Higher Mathematics, 3nd edition, Peter Fletcher,
C. Wayne Patty, Brooks Cole, 1995, ISBN: 053495166X.
Outline:
 To be determined, one possibility follows.
chapter
topic
days

1
2
3
4
5
7

Logic and the Language of Proofs (1-5)
Sets (1-2)
Mathematical Induction (1-5)
Relations and Orders (1-5)
Functions (1,2,5,6)
Cardinality (1-5,7)

 5
2
4
5
5
6
  One Hour Tests 4
  31