# US Mathematics

The study of mathematics encompasses material from the factual to the theoretical, and the Mathematics Department designs its program to contribute to both the common and the special needs of each student. It teaches discipline and principles of logic which may be applied to both higher levels of mathematics and to new fields of study.

These tenets are fundamental to our curriculum:

• That principles of sound algebra are emphasized in all courses, that analytic manipulations in arithmetic and algebra are a priority and that technology is presented to further extend analysis and understanding
• That mathematics is inherently cumulative, so understanding the basics is essential for further success in this sequential discipline.
• That all courses should involve interpreting results, dealing with abstractions and developing generalizations, independent thinking and value estimations.
• That visual representation through graphing via transformations is paramount to understanding functions and relations.

## Advanced Topics in Math Honors

Advanced Topics in Mathematics is a one-semester course, which follows Multivariate Calculus. Selected by the students and the instructor, the topic for the semester will be one of the following: Linear Algebra, Differential Equations, Cryptography, Number Theory or Game Theory.

## Algebra II

Algebra II is designed to reinforce and extend the concepts presented in Algebra I. Topics include solutions to all algebraic functions as well as their graphical analysis. Polynomials and the Fundamental Theorem of Algebra are studied. The conic relations are studied and presented in graphical form.

## Algebra II Honors

All topics presented in Algebra II are covered in greater depth and at an accelerated pace. Sequences and series; matrix and linear algebra; statistics; probability; and exponential and logarithmic functions are introduced.

## Analysis Honors

Analysis Honors is an advanced study of precalculus. The topics are the same as in Precalculus Honors but include the study of: polar coordinates; complex numbers; analytic geometry; matrix and vector algebra; sequences and series; and basic probability and statistics. This course is designed to prepare students for Calculus AP (BC).

## AP Calculus (AB)

The curriculum for AP Calculus (AB) is designed by the College Board. Our purpose is to prepare students for the AP exam so that they may earn credit for the first semester of college-level calculus. Presentation of the material includes the traditional approach to the study of calculus and the more recent reform of using technology to enhance the understanding of calculus. Concepts of differential and integral calculus are developed through an analytic, graphical and numerical presentation; emphasis is on applications.

## AP Calculus (BC)

The curriculum for AP Calculus (BC) is designed by the College Board. Our purpose is to prepare students for the AP exam so that they may earn credit for a full year of college-level calculus. The BC course includes all of the topics of the AB course and extends the applications to include Taylor series, vector functions and parametric and polar curves.

## AP Statistics

AP Statistics is a yearlong college-level introductory statistics course. No understanding of calculus is required. Topics covered include: exploratory data analysis; experimental and sampling design; regression analysis; confidence intervals; and hypothesis tests. Emphasis is placed on understanding key concepts and not on memorizing complicated formulas.

## Calculus Honors

Calculus Honors covers the fundamental concepts of differential and integral calculus but is less rigorous than the AP courses. Initially, concepts and applications are introduced by study of the algebraic functions; later, the transcendental functions are presented. Emphasis is on intuitive understanding of calculus, not on formal proof. Technology is used whenever it enhances the study of the concepts.

## Discrete Mathematics

The Discrete Math course is one distinct semester and may be followed in the spring by Probability and Statistics. The two semesters are independent, as Discrete Math is a stand-alone course and not a pre-requisite for the second-semester Probability and Statistics course. Students work in small groups or individually to solve theoretical and real-life problems, communicate useful mathematical reasoning and employ technology to assist in decision-making. Topics covered include: Election Theory and Fair Division; Matrix Applications; Graph Theory including Circuits, Paths, Trees and Graph Coloring; Counting techniques; Markov Chains; and Game Theory.

## Geometry CP/Honors

Geometry is presented as a formal deductive process. Students study basic definitions and postulates and derive theorems. Student-designed proofs are emphasized in the first semester. The physical attributes of two- and three-dimensional figures are studied. Problem solving includes the proper use of algebraic principles and includes irrational numbers. This Euclidean approach includes congruence, similarity, parallelism, perpendicularity and right-triangle trigonometry. In the honors-level course, all topics are covered in greater depth and at an accelerated pace; this course also extends the formal proof throughout both semesters.

## Multivariate Calculus

Multivariate Calculus is a one-semester course completing the standard three-semester calculus sequence. It is open to students who have completed Calculus AP (BC). Topics covered include basic vector calculus, partial derivatives, multiple integrals, line integrals and surface integrals. The course ends with a discussion of topics such as Green’s, Stokes’ and Divergence Theorems.

## Precalculus

Precalculus is designed to develop a sound understanding of the topics in algebra and trigonometry needed for success in later courses, particularly the study of calculus. Additional topics include exponential and logarithmic functions as well as solving systems of equations through matrices; probability and statistics are introduced. Students become proficient in using the TI graphing calculator.

## Precalculus Honors

Precalculus Honors is a mid-level honors course emphasizing problem solving and analytical skills. Concepts explored include function theory and extensive graphing. The transcendental functions such as trigonometric, inverse trigonometric, exponential and logarithmic functions are studied in depth with an emphasis on graphing.

## Probability and Statistics

Probability and Statistics, a one-semester course, introduces the basic notions of probability and its applications to data analysis. Topics include counting rules, conditional probability, normal distribution with confidence intervals and hypothesis testing. The statistics portion covers descriptive statistics and data representations. The course emphasizes technology heavily.

## Mathematics Department ### Ms. Kimberly Goodstadt

US Math Teacher ### Ms. Diane Hagner

US Math Teacher ### Ms. Jewell Marable

US Math Teacher, US Transitions Advisor ### Mr. Mathew Marsico

US Math Teacher ### Dr. Heather McCloskey

US Math Teacher ### Mr. Jason Smith

US Math Teacher ### Mr. Gus Whyte

US Math Chairperson, US Math Teacher, US History Teacher ### Mrs. Krista Wilhelmsen

Dean Class of 2021, US Math Teacher