Online BS in Mathematics Curriculum

Prerequisite: MATH-152. This is the third course of the calculus sequence. Topics include vector-valued functions; partial derivatives and applications; multiple integrals and applications; double integrals in polar form; substitutions in multiple integrals; line integrals; Green's Theorem in the plane; surface integrals; Stoke’s Theorem.

This course introduces the basic mathematical theory and proofs of the fundamental theorems and formulas in calculus applications. The course prepares students for the demand of advanced courses while giving students an opportunity to witness and participate in the intrinsic beauty of formal mathematical thought. Topics include logic; mathematical inductions; properties of real numbers; theory of functions; set theory; basic study of calculus theory; further discussions of power series and Taylor’s theorem.rals; Green’s Theorem in the plane; surface integrals; Stoke’s Theorem.

This course covers fundamental principles of number theory. Topics include primes and composites; divisors and multiples, divisibility, remainders; the Euclidean Algorithm; the fundamental theorem of arithmetic; congruencies and applications of congruencies; and continued fractions.

This one semester course is designed to introduce the students to the fundamental concepts underlying the study of linear algebra. Topics include matrix algebra; systems of linear equations; vector spaces and subspaces; basis and dimensions; orthogonality; determinants; eigenvalues and eigenvectors; diagonalization of matrices; and linear transformations.

This course introduces the use of mathematical modeling based on calculus and differential equations. Topics include first-order differential equations; Euler’s method and Runge-Kutta method; linear equations of higher order; non-linear differential equations; systems of equations; transforms; and numerical methods. Practical applications are emphasized and computers will be employed to illustrate the underlying mathematical principles.

Prerequisite: MATH-151 or AP Calculus. This is the first in a sequence of two one-semester courses on probability. Topics include basic probability concepts, conditional probability, Bayes Theorem, distribution of random variables; moments, moment generating functions, percentiles, mode, skewness, univariate transformations, discrete distributions (binomial, uniform, hypergeometric, geometric, negative binomial, Poisson), and continuous distributions (uniform, exponential). MATH 370 and MATH 371 (along with Calculus) cover all of the learning objectives contained in Examination P (Probability) of the Society of Actuaries.

Prerequisite: MATH-370. This course should be taken in sequence with MATH 370. Topics include continuous distributions and their applications; uniform distribution, exponential distribution, Gamma distribution, normal distribution and others; central limit theorem; order statistics; mixed distributions; multivariate distributions; marginal distributions; conditional distributions; joint moment generating functions; double expectation theorems. MATH 370 and MATH 371 (along with Calculus) cover all of the learning objectives contained in Examination P (Probability) of the Society of Actuaries.

Prerequisite: MATH-371. This course introduces students to basic concepts of inference and main methods of estimation. Topics include statistical inferences such as point and interval estimation of parameters, statistical hypotheses and statistical tests; inferences for single samples; inference for two samples; inferences for proportion and count data; and advance estimation methods including Moment, percentile matching and Maximum Likelihood. This course emphasizes the applications of the theory to statistics and estimation. This is a calculus-based one semester course. Project based learning is used to help students develop effective problem solving skills and effective collaboration skills. Students who receive a B- or higher in this course are eligible to receive VEE (Validation by Education Experience) credit from the Society of Actuaries in Mathematical Statistics.

Credits: Three (3) Prerequisite Course: MATH 251. The fundamental Analysis course will cover topics both in real analysis and complex analysis. Topics covered in real analysis include properties of the real numbers, ideas of sets, functions, theory of limits, metric spaces, continuous functions, differentiation, Riemann integration, the method of successive approximations, partial differentiation, and multiple integrals. Topics in complex analysis will cover complex numbers, complex plane with particular emphasis on Cauchy's Theorem and the calculus of residues.

Optimization is an essential and important technique for solving problems in many disciplines. Topics covered will be linear programming, infeasible linear programming, unbounded linear programming, pivoting and tableaus, integer programming, solving optimization problems on graphs, shortest path problem, minimum cost perfect matching, understanding the formulation of nonlinear programming, traveling salesmen problem. Modern, real-world examples motivate the theory throughout the course. Students will use MATLAB and work on projects to better understand the concepts learned.

Credits: Three (3) Prerequisite: MATH 316. A first introduction to abstract algebra through group theory with an emphasis on concrete examples. The course will introduce groups, subgroups, homomorphisms, quotients groups and prove foundational results including Lagrange’s theorem, Cauchy’s theorem, orbit-counting techniques and the classification of finite

Prerequisite: MATH-117. The course develops the core concepts and skills in statistical inference and computational techniques through working on real-world data. The course is to introduce the foundation of data science to entry-level students who have not previously taken statistics or computer science courses.

Prerequisite: MATH-117. Students receive basic training in Microsoft Excel. A variety of real-life math models will provide the context for developing spreadsheet proficiency, including functions and formulas, pivotal tables, statistical analysis, numerical solutions, optimization and graphical output. Other areas to be covered include database applications and basic application programming techniques.

Prerequisite/Corequisitie: ACSC/MATH 151 This course covers practical issues in data analysis and graphics that includes programming in R, debugging R codes, Jupyter Notebook, cloud computing, data exploration and data visualization. Project based learning is used to help students develop effective problem solving skills and effective collaboration skills.

Prerequisite/Corequisitie: ACSC/MATH 151 This course covers practical issues in data analysis and graphics that includes programming in Python, debugging Python codes, Jupyter Notebook, cloud computing, data exploration and data visualization. Project based learning is used to help students develop effective problem solving skills and effective collaboration skills.

Prerequisite/Corequisite: ACSC/MATH 151 This course covers practical issues in relational database systems that include creating a database, updating data, retrieving data and saving data in the database. Project-based learning is used to help students develop effective problem-solving skills and effective collaboration skills.

The topics will be covered in this course include: how machine learning differs from traditional programming techniques, data manipulation and analysis, some basic coding skills and an introduction to some of the tools available for data scientists. Specific application techniques will include the following (as time permits): data acquisition, classification, regression, overfitting, supervised and unsupervised training, normalization, distance metrics, k-means clustering, error calculation, optimization training, tree-based algorithms (including random forests), frequent item sets and recommender systems, sentiment analysis, neural networks, genetic algorithms, visualizations, and deep learning (including an introduction to convolutional neural networks and generative adversarial networks).