Sara Marie Bodenstein, MDiv., Duke University
Clint Givens, Ph.D., University of California at Los Angeles
David Kighuradze, Ph.D., Oklahoma State University
Frank Wang, Ph.D., Massachusetts Institute of Technology

Precalculus I | One semester (1/2 unit of credit)

This course provides the background in Euclidean geometry necessary for Precalculus III.  Some topics from trigonometry and algebra are included; however, the major emphasis is on geometry.

Precalculus II | One semester (1/2 unit of credit)

This course is for students who have completed Algebra I and Geometry and provides the background for Precalculus III.  Students will acquire familiarity and skills with zeroes of polynomial and rational functions, radicals, complex numbers, inequalities, graphing, and exponential and logarithmic functions.

Precalculus III | One semester (1/2 unit of credit)

This course is for students who have completed Algebra I and II and Geometry at their home high school or Precalculus I or II, as appropriate, at OSSM.  Precalculus III covers the elements of trigonometry essential for the study of advanced mathematics.  In addition to trigonometry, students study functional analysis, conic sections, polar coordinates, parametric equations, systems of quadratics, complex numbers in polar form, sequences and series, and probability.

Calculus | Two semesters (1 unit of credit)

This is the standard course that covers main concepts of differentiation and integration on functions of one real variable including related topics such as limits and infinite series. Definitions of derivative and integral are given along with main methods of computing derivatives and integrals. Some of the applications include maxima and minima problems, finding volume and surface area of solids of revolution, work and fluid force, and others. The course prepares students for the Advanced Placement exams (“AB” or “BC”) and for entry into most basic junior-level college mathematics courses.

Prerequisites: Precalculus or satisfactory placement test score

Multivariate Calculus | One semester (1/2 unit of credit)

This course introduces the students to operations of differentiation and integration on functions of several real variables. Topics to be presented include parametric curves, vectors, vector functions, surfaces, gradient and directional derivatives, La Grange multipliers, multiple integrals, line and surface integrals.

Prerequisites: Calculus

Differential Equations | One semester (1/2 unit of credit)

This course covers various types of differential equations of first order and higher order with constant coefficients, systems of linear differential equations, inverse differential operators, the LaPlace transformation, power series solutions, and Fourier series solutions.

Prerequisites: Calculus

Number Theory | One semester (1/2 unit of credit)

Students investigate mathematical induction, the binomial theorem, divisibility tests, prime numbers, the Goldbach conjecture, congruences, Fermat’s theorems, Euler’s theorems, Pythagorean triples, Fibonacci numbers, and continued fractions.  By permission of instructor.

Geometrics | One semester (1/2 unit of credit)

This course is a formal approach to Euclidean, projective, and Lobatchevsky geometries.  By permission of Instructor.

Topology | One semester (1/2 unit of credit)

This introduction to topological spaces includes the study of continuity, compactness, separation properties, connectedness, and metric spaces.  By permission of instructor. 

Real Analysis | One semester (1/2 unit of credit)

In this course, the properties of real numbers are analyzed on a rigorous mathematical level. Many results and theorems from elementary
calculus are proved. New topics needed in more advanced mathematical courses are covered, including uniform continuity of functions, point set theory, compactness, and uniform convergence.  By permission of instructor.

Foundations of Mathematics | One semester (1/2 unit of credit)

This course is a formal introduction to axiomatic set theory and arithmetic primitives.  Topics presented include the development of numbers (integers, rationals, reals, complex), cardinality, ordinality, and transfinite numbers. By permission of instructor. 

Special Advanced Problems | One semester (1/2 unit of credit)

This course is designed specifically for students who have a strong background and aptitude in mathematics, and who show particular interest in mathematical competitions.  Students learn the techniques and skills of problem solving that are not discussed in the precalculus courses by working on challenging problems in the Math League Contest, AMC12, AIME, USAMO. In addition to the topics in algebra, geometry, trigonometry, combinatorics and probability, the course covers various topics in elementary number theory such as The Euclidean Algorithm, Diophantine Equations, The Fundamental Theorem of Arithmetic, Primes and Congruence.  By permission of instructor.

Probability and Statistics | One semester (1/2 unit of credit)

This course introduces students to the mathematical theory of probability, including basic probability laws, discrete and continuous probability distributions, conditional probability, and mathematical expectation. It also covers elementary descriptive and inferential statistics, including numerical and graphical data analysis, normal distribution, sampling and bias, experimental design, confidence intervals, significance tests, and simple linear regression.

Linear Algebra | One semester (1/2 unit of credit)

In this course, students investigate foundational topics in linear algebra, including systems of linear equations and matrices; determinants; vectors, lines, and planes in 2 and 3 dimensions; vector spaces, subspaces, linear independence, bases; inner product spaces; eigenvalues and eigenvectors; and linear transformations.