Sara Marie Bodenstein, MDiv., Duke University
Martin Carlson, Ph.D., University of Oklahoma
David Kighuradze, Ph.D., Oklahoma State University
David Tu, Ph.D., University of California, Davis
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.
This course 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.
Prerequisites: Precalculus II
This course introduces students to the foundational elements of differential calculus, including limits, differentiation, and integration on functions of one real variable. Various applications are covered, including related rates problems, maxima and minima problems, areas under curves, and volume of solids.
Prerequisites: Precalculus III
This course covers techniques of integration, improper integrals, infinite sequences and series and their convergence properties, parametric representation of curves, and polar coordinates. Students who have completed both Calculus I and Calculus II should be well-prepared for the AP Calculus AB or BC exam.
Prerequisites: Calculus I
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 II
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.
Prerequisites: Calculus II or permission of the instructor.
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 II
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.
Prerequisites: Precalculus II
This course is designed for students who have mastered introductory calculus and want to deepen their understanding with an emphasis on mathematical reasoning, proof-writing, and the development of strong analytical skills. The course explores advanced techniques of integration, Fourier transform, infinite series and convergence tests, multivariable calculus topics, and the major theorems of vector calculus: Green’s, Stokes’, and the Divergence Theorem. Alongside these theoretical components, students will examine real-world applications in fields such as physics, engineering, and economics.
Prerequisites: Multivariate Calculus
This course covers the theory of functions of a complex variable, extending calculus concepts to the complex plane. Topics include holomorphic functions, Cauchy-Riemann equations, Cauchy’s integral formula, Laurent series, and the Residues theorem.
Prerequisites: Multivariate Calculus
This course is an introduction to various topics in abstract mathematics, including set theory, abstract algebra, and number theory. Topics will be explored with mathematical rigor, reaching subjects such as set cardinality and unique prime factorization of Gaussian integers. Additional topics may be added according to student interest. Students will engage in the active creation of mathematics rather than passively observing it, which includes forming conjectures, writing proofs, and presenting solutions to the class.
Prerequisites: Calculus I and permission of the instructor.
This course introduces students to elementary number theory. Topics presented will include mathematical induction, the binomial theorem, divisibility tests, prime numbers, congruences, Fermat’s theorems, Euler’s theorems, Pythagorean triples, Fibonacci numbers, and continued fractions.
Prerequisites: Precalculus III and permission of the instructor.
This course is for students with a strong background and aptitude in mathematics, and who show particular interest in math competitions. Students learn problem-solving techniques above and beyond those covered in typical precalculus courses by working on challenging problems from contests such as Oklahoma Math League, AMC 12, AIME, Purple Comet, and others. General topic areas covered will include algebra, geometry, trigonometry, combinatorics, probability, and elementary number theory. Course may be repeated with permission of instructor.
