7a. Prerequisite(s): (Course and/or other preparation/experience that is REQUIRED to be completed previous to enrollment in this course.)

Completion of Math. 30 with a grade of "C" or better

7b. Co-requisite(s):  (Courses and/or other preparation that is REQUIRED to be taken concurrently with this course.)

7c. Advisory: (Minimum preparation RECOMMENDED in order to be successful in this course.  Also known as “Course Advisory”.)

9b. Catalog Description:

Study of set theory, relations and functions, logic, combinatorics and probability, algorithms, computability, matrix algebra, graph theory, recurrence relations, number theory including modular arithmetic. Various forms of mathematical proof are developed: proof by induction, proof by contradiction.

10. Student Performance Outcomes: (Outcomes for all credit courses must indicate that students will learn critical thinking and will be able to apply concepts at college level.  Outcomes must be related to items listed in Section 11.)

1. create mathematical proofs directly, indirectly, and by contradiction;
2. use mathematical induction to create a mathematical proof;
3. create a mathematical proof with truth tables and logical equivalences;
4. translate mathematical statements using universal and existential quantifiers;
5. use sets to organize and quantify data;
6. create an algorithm using pseudocode;
7. evaluate a series;
8. model using permutations and combinations and numerically evaluate appropriate applied problems;
9. model using probabilities, including conditional probabilities;
10. solve counting problems using a generating function;
11. assess that a relation is an equivalence relation;
12. create a graph and a tree to describe the structure of a system;
13. use Boolean algebra to mathematically model electronic circuits;
14. verify functions are one-to-one and onto;
15. use matrices to solve applied problems.

11. Course Content Outline: (Provides a comprehensive, sequential outline of the course content, including all major subject matter and the specific body of knowledge covered.)

I. Predicate Calculus
A. Propositional Equivalences
B. Universal and Existential Quantifiers
II. Proofs
A. Counterexample
B. Direct
C. Indirect
D. Contradiction
E. Mathematical Induction
F. Truth Tables
G. Logical Equivalences
III. Algorithms
A. Complexity
B. Growth
C. The Division Algorithm
D. The Euclidean Algorithm
E. Number Bases
IV. Counting Principles
A. Combinatorics
B. Generating Functions
C. Difference Equations
V. Probability
A. Conditional Probability
B. Independence
C. Expected Value
VI. Relations
A. Equivalence Relation
VII. Graphs and Trees
A. Euler and Hamiltonian Paths
B. Shortest Distance Applications
VIII. Boolean Algebra
A. Logic Gates and Switching Circuits
IX. Matrices
A. Operations
B. Applications
C. Systems of Equations

12. Typical Assignments: (List types of assignments, including library assignments.)

a. Reading Assignments: (Submit at least 2 examples)

Throughout the course, read assigned topics from text. For example, how to verify a formula by mathematical induction.

Search the library or the internet for applications of the golden ratio and the fibonacci sequence.

b. Writing, Problem Solving or Performance: (Submit at least 2 examples)

Throughout the course, write mathematical proofs. For example, given a function f, prove that the image of the intersection of two sets is a subset of the intersection of the images of those two sets.

Complete homework assignments including exercise sets from the text.

c. Other (Terms projects, research papers, portfolios, etc.)

SECTION D

SECTION E

SECTION F

SECTION G