I. COURSE IDENTIFICATION

A. DEPARTMENT: MATHEMATICS

COURSE: ADVANCED MATHEMATICS

SUBJECT: SYLLABUS

DATE: 11/4/97

SUBMITTED BY: MATTHEW SCHLAWIN

B. A year long course for Juniors or Seniors with above average ability in Algebra II.

C. Recommended class size - Optimum 20, Maximum 30

II. COURSE OBJECTIVES

A. To further develop the special God-given mental abilities that some students with which some students have been blessed

B. To increase the students' level of logical thinking.

C. To encourage individual research on certain unknown topics.

D. To improve the basic skills of mathematics by working with difficult mathematical concepts.

E. To review ideas on mathematical proof and develop the ability to prove theorems for which no previous proof has been given.

F. To study Trigonometry in depth.

G. To apply previous mathematical learnings to new and different situations.

H. To introduce mathematics which will be learned on the college level.

I. To fulfill certain mathematical requirements of colleges in certain fields.

J. To challenge students who have not previously been challenged.

K. To further acquaint students with examples of writings in the field of mathematics.

L. To become extremely familar with the abilities and limitations of graphing calculators.

III. COURSE CONTENT

A. Review and Extension of functions

1. Functions and relations

2. Domains and Ranges

3. Inverses

4. Composition

B. Periodic Functions Defined on the Basis of the Unit Circle

1. Sin and Cos

2. Identities involving Sin and Cos

3. Tangent, Cotangent, Secant, and Cosecant

4. Identities involving the other circular functions.

C. Graphing the Circular Functions

1. Sin and Cos graph

2. Tan, Cot, Sec, and Cos graphs

3. Studying the sums of circular functions

4. Applications to uniform circular motion

D. Studying the Inverse Functions

1. Inverse functions derived from sin and cos

2. Solving equations using inverse functions

3. Inverse functions based on tan, cot, cos and sec.

4. Solving equations based on the other circular functions

E. Trigonometry and its Relationship to the Circular Functions

1. Relating arc length to angle measure

2. Trigonometric functions and their values

3. Working with identities

F. Applications of Trigonometry to the Study of Triangles

1. Law of Cosines developed and applied.

2. Law of Sines developed and applied

3. Working with right triangles

4. Related formulas for determining area

G. Complex Numbers and Polar Coordinates

1. Review of complex numbers and study them as ordered pairs

2. Polar coordinated defined and graphing of simple problems

3. Application of polar coordinates to complex numbers and D'Moivre's Theorem.

H. Mathematical Study of Series

1. Develop and apply definition of a limit

2. Develop and apply the concept of a derivative

3. Graph higher order polynomials

I. Mathematical study of vectors

1. Vectors as ordered pairs

2. Finding angles in standard position through Trig.

3. Applications of vectors to practical problems

IV. COURSE METHOD AND MATERIALS

A. This is a year long course, classified as honors

B. This course is recommended for any student who is college-bound and is planning to take college courses which are in any way related to mathematics

C. This is a lecture type course

D. Graphing calculators are used heavily throughout this course.