#geometry Geometry This is a one semester accelerated course in Euclidean Geometry for students with a solid background in Algebra. In addition to the content of a standard year long Geometry course, problem solving, conjecture, and proof are emphasized. #mi1 Mathematican Investigations 1 Mathematical Investigations is a four-semester sequence of courses which integrates topics from all areas of pre-calculus mathematics. Throughout the sequence, students will be expected to explore mathematical concepts, make conjectures and present logical, valid arguments for mathematical assertions. Both written and oral forms of communication are emphasized. Prior to entry into the Mathematical Investigations sequence, the student must demonstrate a strong background in Algebra, including a thorough understanding of the underlying concepts, a demonstrated ability with algebraic skills, and schemata which encourages mathematical thinking. #mi2 Mathematical Investigations 2 The second course in this sequence, MI-2, will concentrate on the study of matrices, linear relationships, functions, and arithmetic and geometric sequences. Exponential functions are introduced. #mi3 Mathematical Investigations 3 MI-3 is the third semester of the Mathematical Investigations sequence. MI-3 builds on MI-2, extending the concept of function and applications to include polynomials, rational functions, logarithmic functions, and trigonometric functions. #mi4 Mathematical Investigations 4 MI-4 is the fourth semester of the Mathematical Investigations sequence. This semester will emphasize sequences and series, vectors, advanced trigonometry, conics, topics selected from combinatorics, Binomial Theorem and mathematical induction. #ab1 AB Calculus 1 AB Calculus is a two semester sequence which includes the concepts presented in the Advanced Placement AB Calculus syllabus. The first semester course discusses limits, derivatives and their applications, and an introduction to integration. #ab2 AB Calculus 2 The second semester of this sequence will include additional topics from the Advanced Placement AB Calculus syllabus with a concentration on the integral and its applications. Students completing AB Calculus I and AB Calculus II will have completed the equivalent of a semester of college level calculus. #bc1 BC Calculus 1 BC Calc is a three semester sequence which includes the material covered in the Advanced Placement BC Calculus syllabus. This course will cover the foundations of calculus including concepts and applications of rates of change, derivatives, antiderivatives, and limits. With help from technology these will be seen from graphical, numerical, and analytic points of view. #bc2 BC Calculus 2 This second course will continue the study of derivatives and begin work on concepts and applications of integrals. Technology will be an important part of the development of the course. #bc3 BC Calculus 3 The third course of the sequence will conclude the material covered in the Advanced Placement BC Calculus syllabus. Topics will include sequences and series, differential equations, and polar graphs. #adgeom Advanced Geometry This course is a study of advanced topics in geometry selected from such areas as: points of concurrence, cevians, the golden mean, fractals, matrix transformations, geometric averages, non-Euclidean geometries, geometric probability, modeling, spirals, the theorems of Ceva, Menelaus, Pascal, Desargues, and Pappus. The course emphasizes mathematical connections through individual and group explorations, discussions and problem solving. #data Data Analysis This is a very hands-on course in elementary statistics. Descriptive statistics and graphical displays for single and bi-variate data will be created and analyzed. Students will also analyze ways in which data is used and displayed in public documents. Several group and individual projects are required. Additional topics will be selected from probability, discrete and continuous distributions, regression analysis and correlation, design of experiments, and hypothesis testing. #diffeq Differential Equations The theory of differential equations is interesting as a mathematical topic and has special relevance because it describes a surprising diversity of real world situations. In this course, we will investigate the behavior of solutions to linear and nonlinear differential equations. Special emphasis will be given to applications in the physical and biological sciences. Upon completion of this course, a student will be able to choose, troubleshoot, customize, or develop a variety of differential equation modeling schemes to suit his or her own particular needs. #mathematica Exploring Math Topics Using Mathematica Students will learn to use the Mathematica computer software environment to explore mathematical topics from different perspectives. Prior experience with the software is not necessary. #mvc Multi-Variable Calculus Multi-Variable Calculus will apply the tools of calculus to functions of several variables. Topics will include the algebra and geometry of vectors, a study of functions of several variables, applications of partial derivatives, multiple integrals, line and surface integrals, and (time permitting) Green's, Stokes' and Gauss' Theorems. #number Number Theory Number Theory challenges students to question the number systems they have used all their lives. The integers are defined axiomatically, and familiar properties of arithmetic are proven. Exploration then turns to divisibility, primes, and the Fundamental Theorem of Arithmetic, the GCD, and linear diophantine equations. Linear congruence problems and multiple congruences (Chinese Remainder Theorem) are followed by special congruences (Theorems of Wilson and Euler-Fermat). This is then used to study decimal expansions of rational and real numbers. Further topics may include primality testing, continued fractions, introductory cryptography, and quadratic reciprocity. This course is centered around a dual emphasis on calculation techniques and rigorous proof. #ps Problem Solving In this course, students will learn how to apply a broad range of problem solving techniques and strategies while making inter and intra-disciplinary mathematical connections. The course will emphasize both individual and group investigations and explorations. Students may not receive credit for both Problem Solving and Advanced Problem Solving. #aps Advanced Problem Solving The course will emphasize advanced techniques and strategies used at the national and international levels of problem solving, Mathematical Olympiads. Methods of proof and validation will be highlighted in presenting formal mathematical solutions to unconventional, non-routine, essay-type problems. The course content will focus upon topics from advanced geometry, combinatorics, theory of equations, series, sequences, trigonometry and number theory. #discrete Discrete Mathematics The main emphasis of study will include topics of social applications, matrices, graph theory, recursion, techniques of counting, permutations, combinatorics, and probability. A major emphasis will be both individual and group investigations and explorations. #alstruct Algebraic Structures

Algebraic structures I and II are advanced course offerings for students working at a level beyond Calculus. One of the two course options described below will be chosen by the mathematics department to be taught each second semester. Students taking the course for the first time should sign up for enrollment in Algebraic Structures I (1160). Students who have already received credit for course number 1160 should sign up for enrollment in Algebraic Structures II (1161) after discussion with instructor or department coordinator.

Option 1 - Linear Algebra

This course concentrates on the theory of simultaneous linear equations. Gaussian elimination is used as a tool to solve linear systems and to investigate the subspace structure of a matrix (kernel, range, etc.) Extensions of these ideas include orthogonality and least squares. Determinants are examined from several angles. Eigenvalues and eigenvectors are introduced, including a discussion of special matrices (symmetric, unitary, normal, etc.) The course also takes an abstract approach, looking at general linear transformations on finite dimensional vector spaces, culminating in the Jordan canonical form.

Option 2 - Abstract Algebra

The content of this course if flexible, but is generally an introduction to abstract algebra. Students learn about groups, subgroups, homomorphisms, and the structure of various groups (such as the structure theorem for finitely generated Abelian groups, the Sylow theorems, etc.) Students also investigate the basics of rings. Ring topics include ideals and homomorphisms; PIDs, UFDs, and Euclidean domains; fields and (time permitting) field extensions including applications such as constructibility. All aspects of the course are presented with full mathematical rigor, and students are expected to produce proofs of equivalent quality to mathematics majors at a university. #asm Assembly Language Programming This course will introduce the students to the specifics of assembly language programming in the context of the 80x88 family of computers. Approximately half of the semester will be spent learning the language by writing programs which manipulate text and numeric data. The remainder of the semester will be spent writing applications programs. Depending on student interest and background, those applications might include, but are not limited to, the following: a communications program between two computers, an interactive game using ASCII characters on the display, controlling and L.E.D. clock, controlling the traffic lights in an intersection, a disk utility program, and interfacing assembly language routines with high level programs. #compsem Computer Seminar This course will study advanced computer science topics including object oriented programming. Students will be expected to complete several group and individual projects, including a major program. #apcs AP Computer Science This course will complete the AP Computer Science AB syllabus. Topics may include: pointer variables, recursion, stacks, queues, trees, linked lists, advanced programming techniques including advanced sorts and searches. A major focus of the course will be an analysis of the APCS case study. #cpp Introduction to Programming Using C++ This course is an introduction of programming and computer science using C++ language. Top down approach to algorithmic design and structural, object oriented programming will be emphasized.