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.

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). This course is calculus—based.

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.

The fundamental analysis course will cover topics both in real analysis and complex analysis. Topics covered in real analysis include sets, properties of the real numbers, compactness of closed intervals, the countability compact property of closed intervals, continuous functions, completeness of the real number line. Topics in complex analysis will cover complex numbers, complex plane, Cauchy Reimann equations, and Cauchy's Integral Theorem, the concept of the periodic function, Fourier series, Fourier transformation.

Optimization is an essential and important technique for solving problems in many disciplines. Topics covered in the course will be Introduction to Modeling, Linear Programming, The Simplex Method, Network Models, Integer Programming, and Non-Linear Programming. Modern, real-world examples motivate the theory throughout the course.

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.

This course covers practical issues in data analysis and graphics such as programming in R, debugging R code, 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.

This course covers data types, statements, expressions, control flow, top Python core libraries (NumPy, SciPy, Pandas, Matplotlib and Seaborn) and modeling libraries (Statsmodels and Scikit-learn). Project based learning is used to help students develop effective problem solving skills and effective collaboration skills. Cross-Listed: DSCI-503

This course is for students who want to enhance their SQL skills through exploring real-world examples. Topics covered include but are not limited to pattern-matching using regular expressions, analytical functions, and common table expressions. Students are expected to be able to construct advanced SQL queries to retrieve desired information from the database and solve real-world problems Cross-listed: DSCI-504

This is an introductory course in machine learning intended primarily for students majoring or minoring in Mathematics, Data Science or Actuarial Science. This course may also be useful for those using predictive modeling techniques in business, economics or research applications. The main focus of this course is to understand the basic operations and applications of what we currently call machine learning. This course will cover material from several sources. A few main topics that will be covered 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). Cross-Listed: DSCI-508

This course introduces students to basic discrete mathematics concepts. Topics include logic, elementary number theory methods, number systems, sets, functions and relations, counting and probability, theories of graphs and trees, and analysis of algorithm efficiency.

This course is required for Secondary Education students specializing in math. It is also taken by math majors who are interested in geometry or who want to gain experience in writing proofs before they attempt more advanced math courses. Topics include triangles congruence, polygons, Pythagorean Theorem, formal/informal proofs, coordinate systems, conic sections, and transformations.

This course focuses on model development, interpretation, understanding assumptions and evaluation of competing models. Topics include the basics of statistical learning, linear models, and time series models. This course covers a majority of the learning objectives for the Society of Actuaries (SOA) examination SRM (Statistics for Risk Modeling).

This class is an introduction to the SAS programming language. Topics include reading, exporting, sorting, printing, and summarizing data; modifying and combining data sets; writing flexible code with the SAS macro facility; visualizing data; and performing descriptive and basic statistical analyses such as Chi-square tests, T-Tests, ANOVA, and regression. Project based learning is used to help students develop effective problem solving skills and effective collaboration skills. Cross-Listed: DSCI-507

This course covers text analytics, the practice of extracting useful information hidden in unstructured text such as social media, emails and web pages using Python. Topics include working with corpora, transformations, metadata management, term document matrices, word clouds, and topic models. Project based learning is used to help students develop effective problem solving skills and effective collaboration skills.

This course covers principles of experiments and basic statistics using R/SAS. Topics include analysis of variance, different designs, analysis of covariance, mixed model, categorical data analysis , survey data analysis, sample size and power analysis and model comparison. Project based learning is used to help students develop effective problem solving skills and effective collaboration skills.

This course is intended for students with introductory experience in SQL, R, and Excel. In this course, students will learn how to connect SQL Server to tools like Excel, R, and Tableau, and how to leverage the database engine to manipulate large amounts of data for data analysis tasks. Students will learn how to create analytical plots in Excel and R and how to follow best practices for creating report-quality graphs and presentations. Students will learn to use R Markdown so that their analysis follows the reproducible research paradigm. Finally, students will learn to build reporting and analytics dashboards in Shiny and Tableau. This course will be project-based. By the end of the class, the students will have a portfolio of analytical work completed inside and outside of class.

This course introduces students to fundamental statistical learning techniques that can be applied to real-world business problems. Topics include generalized linear models, tree-based models, clustering methods, and principal components analysis. It trains students to understand key steps and considerations in building predictive models, selecting a best model, and effectively communicating the model results. Project based learning is used to help students develop effective problem solving skills and effective collaboration skills. Cross-listed: DSCI-512