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. Textboook cover
Prerequisites:
Mathematics 251 or departmenatl approval.
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.

Text:
Book of Proof (edition 2.2), Richard Hammack, Virginia Commonwealth University, available from the author for free at www.people.vcu.edu/~rhammack/BookOfProof or as a cheap paper back as ISBN: 978-0-9894721-0-4.
Grade:
  55%   tests (about three one-period tests) 
  20%   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.
Homework:
Homework will be collected the day it is due at at the beginning of the class period--have it ready. You may turn your homework in early. For each hour homework is late, it will lose 5% of its value.
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) 
Outline:
The daily asignments will be handed out in class and will be placed on the homework page above.
chapter
topic
days

1
2
4
5
6
7
8
9
10
11
12

Sets (1-8)
Logic (1-8,9-10)
Direct proof (1–5)
Contrapositive proof (1–3)
Proof by contradiction (1–4)
Proving Non-Conditional Statements (1–4)
Proofs involving sets (1–3)
Disproof (1–3)
Mathematical Induction (1–3)
Relations (1–5)
Functions (1–5)

7
4
2
2
2
1
2
1
3
4
5
  One Hour Tests 4
  41