Courses
1112(F) Geometry I/II (core)
Grade Level: Sophomore/Junior/Senior
Length: One Semester (offered Fall Semester only)
Credit: 0.50
Prerequisite: Initial Placement by Math Department
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. Students will also have the opportunity, using computers, to explore geometry dynamically.
1121(F) Mathematical Investigations I (core)
Grade Level: Sophomore/Junior
Length: One Semester (offered Fall Semester only)
Credit: 0.50
Prerequisite: Initial Placement by Math Department
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.
1123(F) Mathematical Investigations II (core)
1124(S)
Grade Level: Sophomore/Junior/Senior
Length: One Semester
Credit: 0.50
Prerequisite: MI-1 or Initial Placement by Math Department
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.
1125(F) Mathematical Investigations III (core)
1126(S)
Grade Level: Sophomore/Junior/Senior
Length: One Semester
Credit: 0.50
Prerequisite: MI-2 or Initial Placement by Math Department
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.
1127(F) Mathematical Investigations IV (core)
1128(S)
Grade Level: Sophomore/Junior/Senior
Length: One Semester
Credit: 0.50
Prerequisite: MI III or Initial Placement by Math Department
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.
1132(F) AB Calculus I (core)
1133(S)
Grade Level: Sophomore/Junior/Senior
Length: One Semester
Credit: 0.50
Prerequisite: MI IV and recommendation of MI Instructors
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.
1134(F) AB Calculus II (core)
1135(S)
Grade Level: Sophomore/Junior/Senior
Length: One Semester
Credit: 0.50
Prerequisite: AB Calculus I
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 AB Calculus II and I will have completed the equivalent of a semester of college level calculus.
1140(F) BC Calculus I (core)
1141(S)
Grade Level: Sophomore/Junior/Senior
Length: One Semester
Credit: 0.50
Prerequisite: MI IV and recommendation of MI Instructors
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.
1142(F) BC Calculus II (core)
1143(S)
Grade Level: Sophomore/Junior/Senior
Length: One Semester
Credit: 0.50
Prerequisite: BC Calculus I
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.
1144(F) BC Calculus III (core)
1145(S)
Grade Level: Sophomore/Junior/Senior
Length: One Semester
Credit: 0.50
Prerequisite: BC Calculus II
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.
1150 Advanced Geometry
Grade Level: Junior/Senior
Length: One Semester (offered Spring Semester only)
Credit: 0.50 Pass/Fail option
Prerequisites: Math Investigations IV or recommendation of Instructor
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 Geometry’s, 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.
1151 Data Analysis
Grade Level: Junior/Senior
Length: One Semester (offered both Fall and Spring Semesters)
Credit: 0.50 Pass/Fail option
Prerequisite: MI-III or recommendation of Instructor
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. Computer software is used for dynamic modeling of data. 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.
1152(S) Differential Equations
Grade Level: Junior/Senior
Length: One Semester (offered Spring Semester only)
Credit: 0.50 Pass/Fail option
Prerequisite: BC II (or AB II with permission of Instructor)
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.
1153 Exploring Mathematics with Mathematica
Grade Level: Junior/Senior
Length: One Semester [Semester(s) offered based on student interest]
Credit: 0.50 Pass/Fail option
Prerequisite: Mathematical Investigations IV OR MI III and permission of instructor.
Students will learn how to use Mathematica computer software to help model and explore mathematical topics. Much of the course will be project oriented, including creating interactive notebooks and programming, depending upon individual student backgrounds and interests. Students will work with 2D and 3D graphics, colors, and animations. No prior experience with Mathematica or with computer programming is necessary.
1154(F) Multi-Variable Calculus
1155(S)
Grade Level: Junior/Senior
Length: One Semester [Semester(s) offered based on student interest]
Credit: 0.50 Pass/Fail option
Prerequisite: BC Calculus III and recommendation of Instructor
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.
1156 Number Theory
Grade Level: Junior/Senior
Length: One Semester (offered Fall Semester only)
Credit: 0.50 Pass/Fail option
Prerequisite: BC Calc I (which in exceptional cases may be taken concurrently) and permission of Instructor and Mathematics Operational Coordinator
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.
1157 Problem Solving
Grade Level: Junior/Senior
Length: One Semester [Semester(s) offered based on student interest]
Credit: 0.50 Pass/Fail option
Prerequisite: Math Investigations III or recommendation of Instructor
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 will not receive credit for Problem Solving if they have prior credit in Advanced Problem Solving.
1158 Advanced Problem Solving
Grade Level: Junior/Senior
Length: One Semester (offered Fall Semester only)
Credit: 0.50 Pass/Fail option
Prerequisite: BC Calculus I, or permission of instructor; and Mathematics Operational Coordinator. Student should have a very strong score on the AMC contest, though need not be a mathlete.
The course will emphasize advanced problem solving techniques and strategies used on the AIME, ARML, Mandelbrot and AVASC level contests. Methods of proof, derivation, and validation will be highlighted in solutions to non-routine problems. The course content will focus upon topics from advanced geometry, combinatorics, theory of equations, series, sequences, trigonometry and number theory, etc.
1159 Discrete Mathematics
Grade Level: Junior/Senior
Length: One Semester [Semester(s) offered based on student interest]
Credit: 0.50 Pass/Fail option
Prerequisite: Math Investigations III or recommendation of Instructor
The main emphasis of study will include topics of social applications, matrices, graph theory, recursion, techniques of counting, permutations, combinations, and probability. A major emphasis will be both individual and group investigations and explorations.
1160 Introduction to Algebraic Structures I
1161 Introduction to Algebraic Structures II
(Use 1161 only if took 1160 last year.)
Grade Level: Junior/Senior
Length: One Semester (offered Spring Semester only)
Credit: 0.50 Pass/Fail option
Prerequisite: Multi-variable Calculus or Advanced Problem Solving or Number Theory and permission of the Instructor and Mathematics Operational Coordinator.
Algebraic Structures I and II are advanced All 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 othogonality 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 is 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.
1162(F) Advanced Topics in Mathematics
1163(S)
Grade Level: Junior/Senior
Length: One Semester
Credit: 0.50 Pass/Fail option
Prerequisites: Multi-Variable Calculus and one of Advanced Problem Solving, Number Theory, or Algebraic Structures I and permission of Instructor and Mathematics Operational Coordinator
For students who have finished the core mathematics program and for whom there is no other appropriate mathematics course available. Student and instructor will select topics jointly. Past years’ topics have been complex variable, topology, and real analysis. May be used as core mathematics course.
1168 Introduction to Visual Basic
Grade Level: Junior/Senior
Length: One semester [Semester(s) offered based on student interest]
Credit: 0.50 Pass/Fail option
Prerequisites: Math Investigations III or permission of instructor AND no previous computer science coursework.
This course is an introduction to computer programming using the Visual Basic computer language. Visual Basic is intended specifically for students who wish to learn about computer programming but do not have aspirations in computer science related fields. (Any student wishing to take APCS or Computer Seminar must take Intro to Computer Science)
1169 Introduction to Computer Science
Grade Level: Junior/Senior
Length: One Semester (offered both Fall and Spring Semesters)
Credit: 0.50 Pass/Fail Option
Prerequisite: Math Investigations III or recommendation of Instructor
Intro to C.S. is an introduction to programming and computer science using the current APCS language (Java). The course emphasizes programming methodology with an emphasis on problem solving and algorithm development, using object oriented programming. It is intended to feed naturally into APCS (1171)
1171(S) AP Computer Science
Grade Level: Junior/Senior
Length: One Semester (offered Spring Semester only)
Credit: 0.50 Pass/Fail option
Prerequisite: Introduction to C.S. or recommendation of Instructor
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.
1173 Assembly Language Programming
Grade Level: Junior/Senior
Length: One Semester [Semester(s) offered based on student interest]
Credit: 0.50 Pass/Fail option
Prerequisite: Introduction to C.S. or recommendation of Instructor
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 that manipulate text and numeric data. The remainder of the semester will be spent writing application 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 an L.E.D. clock, controlling the traffic lights in an intersection, a disk utility program, and interfacing assembly language routines with high level programs.