Mathematics

This course introduces students to the three fundamental concepts of calculus, using standard and nonstandard algorithms of numbers and quantity, and focus on Fundamental Theorem of Calculus, logarithmic, exponential, and trigonometric functions. Study of limits and continuity, evaluation of limits using algebraic techniques (such as finding the absolute value), numerical approximations, and/or computers, dealing with rational, irrational, real, and complex numbers; study of derivative of elementary functions, physical applications of the derivative including functional representations such as curve sketching (table graphs), rate problems, maximizing and minimizing physical quantities; study of antiderivative, definite integral, the classical
area problem and applications of the definite integral and basic integration techniques.

Continuation of Calculus I; in-depth study of the techniques of integration; study of sequences, infinite series and their convergence/divergence; study of curves described by parametric equation and polar coordinates; study of vector functions; and focus on Fundamental Theorem of Calculus to solve problems involving calculus.

This course covers statistical change, statistical inference, statistical design, organizing, creating, and summarizing data (such as implementing box plots, histograms, cumulative frequency plots), probability concepts, estimation, chance phenomena, simulations, and tests of significance (decision-making).

This course is an introduction to the theory and use of discrete mathematical structures that include quantitative reasoning, mathematical logic, mathematical induction, combinatorics (permutations and combinations), relations, partially ordered systems, graphs, trees, networks, permutations, logic and linear programming (predicate logic), analysis of algorithms, recursion, relationships, Boolean algebras and other algebraic structures, and modeling.

This course extends the concepts of single variable calculus to multivariate functions. Topics include study of vector operations in n-dimensional space; vector-valued functions; differential and integral calculus of multiple variables; using geometry and trigonometry to solve problems involving calculus.

This course is a study of vector operations and spaces, subspaces, and linear transformations as well as quadratic, polynomial, and exponential functions; systems of linear equations; matrix operations, determinants, eigenvalues, and modeling real-world relationships.

This course is a study of algebra as it relates to elementary number theory (such as factorization, primes, and common factors), groups, rings (such as, division rings), integral
domains, and elementary field theory and the relationship between structures of number systems and symbolic calculations, modeling those relationships and operations.

This course is a study of equations of the first order, linear equations of higher order, existence and uniqueness, the LaPlace Transform, numerical methods, applications in order to formulate, represent, and analyze mathematical models derived from real-world contexts.

This course is an extension of discrete mathematical structures that include quantitative reasoning, mathematical logic, mathematical induction, combinatorics (permutations and combinations), relations, partially ordered systems, graphs, trees, networks, permutations, logic
and linear programming (predicate logic), analysis of algorithms, recursion, relationships, Boolean algebras and other algebraic structures, and modeling.

This course is a study of axiomatic systems for affine geometries, translations, dilations, rotations, reflections, and linear transformations, and affine geometries over rings. Topics included in this course are proofs, trigonometry, periodic phenomena, identification, classification into categories, visualization, representation, Euclidean affine geometry, congruence (symmetry) and similarity, measurement, and conics; the course uses formulas to find perimeter, area, surface area, and volume and to solve problems involving geometry, trigonometry, and calculus.

This course emphasizes readings in the historical development perspectives of number systems, algebra, geometry, statistics, probability, calculus, discrete mathematics, and trigonometry featuring diverse cultures in ancient and modern writings. Students will make oral and written presentations to express mathematical understandings and ideas precisely and to demonstrate the interconnectedness among those ideas concerning mathematical thinking based upon the topics discussed in the readings; and the course gives attention to practices of problem solving and reasoning.

This course is a study of number theory, derivatives, and integrals; introduction to special functions, function spaces, and series of functions; methods of writing and understanding
mathematical proofs.