Corequisite

64112 Precalculus I, or 64113 Precalculus II, or 64211 Foundations of Calculus. This course must be taken in conjunction with one of the three corequisite courses.

Description

This course is designed as an honors component to supplement existing course at the precalculus level. The course is intended to provide students with exposure to relevant ideas for future courses in Calculus and/or Statistics. Topics include arithmetic and geometric sequences and sums, infinite series, the binomial theorem, mathematical induction, permutations, combinations, and probability. Critical thinking learning techniques are used to promote a clearer understanding of the logic of the mathematical concepts studied.

Statement of Course Need

Honors courses in mathematics have been developed to provide mathematically talented students the opportunity to obtain a level of rigor not currently available in existing courses. Topics in these courses have been selected to help students develop an appreciation of the origin and evolutionary growth of mathematical ideas from antiquity to the present. These courses have been designed as one-credit components to existing courses. They are intended to both supplement and complement the ideas and topics presented in courses at the level of precalculus, calculus, and statistics.

Student Learning Objective
The student will be able to:

1. Use mathematical assumptions and precise definitions for the purpose of logical reasoning.
2. Demonstrate an understanding of inductive reasoning and the scientific method through the use of mathematical induction proofs.
3. Understand and use the fact that mathematics language does not depend solely on its practical use but that it has an appeal of its own that is similar to poetry or art.

1. Sequences and Sums
   1. Term
   2. Constant Sequence
   3. Recursively Defined Sequence
   4. Fibonacci Sequences
   5. Summation Notation and Index
   6. Partial Sum
2. Arithmetic Sequence
   1. Common Difference
   2. Partial Sum Formulas
3. Geometric Sequence
   1. Common Ratio
   2. Partial Sum Formula
   3. Frequencies of musical notes as an application of geometric sequences
4. Infinite Series
   1. Zeno's Paradoxes on infinity and the Golden Ratio
   2. Convergent and Divergent Series
   3. Infinite Geometric Series
5. The Binomial Theorem
   1. Binomial Coefficients
   2. Properties of the Binomial Expansion
6. Mathematical Induction
   1. Principles of Mathematical Induction
   2. Proof of Binomial Theorem
7. Counting Principle
   1. Permutations
   2. Combinations
8. Probability
   1. Definition of the Probability of an Event
   2. Definition of a Complement
   3. Properties of Probability

   Methods for student Evaluation
   Will vary according to the instructional style of the teaching faculty.
   Lab Fees--None; Date: Jan, 1997, Sponsoring Dept: Mathematics