COURSE SYLLABUS
Ohio Northern University
College of Arts and Sciences
Department of Mathematics and Statistics
Date: Fall 2011
Course Math 2691 Name: Foundations of Mathematics with Problem Solving
Credit hours: 3
Instructor: Staff
Lecture hours/week: 3
Usual Student Level: Junior
Course required of students in: Mathematics
Course frequency per semester/year: Offered yearly; spring semester
Average enrollment per year: 10-15
This course has a prerequisite: Math 1641
Lab hours/week: 0
This course is a prerequisite for: Math 3011, Math 3061, Math 3241,
Math 3411, Math 2611, Math 4211
It is part of the Mathematics Majors Common Cored
Catalogue Description:
An introduction to problem solving strategies and techniques of formal proof.
Course Objectives:
To introduce students to the logic required for mathematical reasoning, geared towards the understanding of the concept of formal proof. To expose the students to a significant number of problem solving strategies and techniques in various areas of mathematics so that they may become proficient problem solvers.
Textbook: A problem solving textbook such as Challenging Mathematical Problems with Elementary
Solutions by A. M. Yaglom and I. M. Yaglom – or other material chosen by the instructor
A Transition to Advanced Mathematics, 6 th Edition by D. Smith, M. Eggen and R. St. Andre.
Outline of content follows:
(see attached)

Course Outline
MATH 2691
Foundations of Mathematics and Problem Solving
TENTATIVE COURSE OUTLINE BY WEEK
1.
Introduction: Problems and Proofs in Plane Geometry
2.
Propositions and Connectives; Predicates and Quantifiers; Mathematical Proofs
3.
Mathematical Proofs (cont.); Types of Proofs
4.
Sets and Set Operations, Extended Set Operations and Indexed families of Sets; Mathematical
Induction
5.
Sequences and Summation; Fibonacci Numbers and Fibonacci Identities; Recurrent Sequences
6.
Identities and Inequalities; Analytic Inequalities; Calculus-based Reasoning in Problem Solving
7.
Cartesian Products and Relations; Equivalence Relations and Partitions; Order Relations
8.
Functions as Relations; Construction of Functions; One-to-one and Onto Functions; Induced Set
Functions
9.
Pigeonhole and Inclusion-Exclusion Principle; Permutations and Combinations; Pascal’s Triangle;
Combinatorial Methods; Combinatorial Identities; Methods of Graph Theory in Problem Solving
10.
Elements of Probabilistic Reasoning in Relation with Combinatorics and Geometry
11.
Equivalent Sets; Countable Sets; Cardinality
12.
Integers and Elementary Number Theory; Prime Numbers; Diophantine Equations; Congruences
13.
Special topics involving Geometrical Reasoning; Geometrical Transformations
14.
Special topics involving Algebra-based Abstract Reasoning
15.
About 3 More Hours for Testing