# Course Descriptions

#### Mathematics Sequence (18 credits)

### MATH 115 Calculus I - 4 credits

Limits, continuity, and differentiation of algebraic, exponential, logarithmic, trigonometric, and inverse trigonometric functions. Sum, product, quotient and chain rule formulas for differentiation. Logarithmic and implicit differentiation. Linearization and differentials. Indeterminate forms and L'Hospital's Rule. Graphing using the first and second derivative. Application of the derivative to optimization and related rates problems. Indefinite and definite integrals. Substitution rule for integration. Application of the definite integral to area problems. Credit is not allowed for both MATH 115/104, MATH 115/114, or MATH 115/111. Prerequisite: grade of "C" or better in MATH 105, or evidence of mastery of college algebra skills and trigonometry

### MATH 116 Calculus II - 4 credits

Applications of integration (areas, volume, work, arc length, surface area), additional techniques of integration, improper integrals, infinite sequences and series, including tests of convergence, power series, Taylor and Maclaurin series. Prerequisite: grade of "C" or better in MATH 114 OR MATH 115.

### MATH 215 Calculus III - 4 credits

Parametric equations, polar coordinates, calculus of functions of several variables and vector-valued functions, including double and triple integrals using various coordinate systems. Prerequisite: grade of "C" or better in MATH 116.

### MATH 135 Discrete Mathematics* - 3 credits

Sets, functions, relations, partial order, methods of propositional logic, introduction to predicate logic, counting, recurrence relations, asymptotic analysis, techniques of proof writing including induction.

### MATH 310 Linear Algebra - 3 credits

Systems of linear equations, matrix operations, determinants, vector spaces and subspaces, linear transformations, change of basis, eigenvalues and eigenvectors, diagonalization, and orthogonality. Prerequisites: grade of "C" or better in MATH 116. Credit is not allowed for both MATH 210 and MATH 310.

_{* Course does not count toward math major}

#### Statistics Core (12 credits)

### MATH 301 Introduction to Probability and Statistics I - 3 credits

Univariate and multivariate probability distributions of discrete and continuous random variables, mathematical expectation, limit theorems, random variable transformations, moment generating functions. Prerequisite: grade of "C" or better in MATH 116.

### MATH 302W Introduction to Probability and Statistics II - 3 credits

Sampling distributions of random variables, confidence intervals, and hypothesis testing for one and two sample settings. ANOVA, simple linear regression, estimation techniques, properties of estimators, likelihood ratio test. Prerequisite: grade of "C" or better in MATH 301. Credit is not allowed for both MATH 302W and MATH 335.

### MATH 325W Applied Statistics with Regression - 3 credits

This course begins with a review of inferential statistics. Emphasis on data collection methods, stating hypotheses, confidence intervals and bootstrapping methods for estimating parameters are introduced. Both traditional and re-sampling methods are demonstrated for testing hypotheses. Additional topics covered are graphical methods for exploring distributions and determining outliers, 1-way and 2- way analysis of variance models using a linear models approach, and linear and multiple regression methods. JMP software is used for demonstrating methods. Prerequisites: grade of "C" or better in MATH 225 or in MATH 301.

### MATH 445 Prediction and Classification Modeling - 3 credits

Classification rates, ROC curves, cross-validation techniques, modern regression methods, data reduction/principle components, stages of biomarker development, and study design issues in cancer and occupational research. Prerequisite: grade of "C" or better in MATH 325W or in MATH 525W.

### MATH 473 Statistical Computing - 3 credits

Generating pseudo-random numbers, Monte Carlo integration, simulation, Bayesian inference, Gibbs sampling, Metropolis sampling, Metropolis-Hastings sampling, the E-M algorithm, multivariate Newton-Raphson maximization. Prerequisites: grade of "C" or better in MATH 302W, and one of COSC 150, COSC 160 or COSC 170.

#### Computer Science Core (12 credits)

### COSC 170 - Computer Programming: Python - 3 credits

This course is an introduction to the Python programming language for the students without prior programming knowledge and experience. Topics include Variables, Expressions, Built-indata types, Sequences, Control Structures, Methods, Objects, Classes, Exceptions, List, Files and Inheritance. Credit is not allowed for COSC 150, COSC 160 and COSC 170. Offered fall and spring.

### COSC 216 - Data Structures in Python - 3 credits

Data abstraction, queues, linked lists, recursion, stacks, trees, string processing, searching and sorting, and hashing. Python API support for data structures. Prerequisite: grade of "C" or better in COSC 170, and either a grade of "C" or better in MATH 135 or concurrent enrollment in MATH 135. Credit is not allowed for COSC 216 and COSC 215. Offered every semester.

### COSC 300 - Algorithms - 3 credits

Algorithm design: divide-and-conquer, greedy algorithms, dynamic programming, reductions; algorithm analysis: asymptotic analysis (big-O), amortized analysis; graph algorithms; complexity classes: NP-completeness, Cook's theorem, NP-complete problems. Prerequisite: grade of "C" or better in COSC 160 and COSC 215 or COSC 170 and COSC 216. Offered fall and spring.

#### Data Science Core (12 credits)

### DTSC 110 Introduction to Data Science

This course introduces students to the growing field of data science through the presentation of introductory concepts in data management, preparation, presentation, and modeling, through an introduction to the computer tools and software commonly used to perform data analytics including R, Python, and SQL, and through a general overview of the machine learning techniques commonly applied to datasets for knowledge discovery. Concepts, techniques, and tools needed to deal with various facets of data science practice, including data collection and integration, exploratory data analysis, descriptive analyses, principles of statistical design and inference, and effective communication, are introduced. Students will gain an understanding of the varied nature of data, their acquisition and preliminary analysis, which provide the requisite skills to succeed in further study and application of the data science field.

### DTSC 220 Data Exploration and Visualization

This course will explore methods for understanding and visualizing data, with a focus on approaches for dealing with large and multidimensional datasets. The objective of this course is to provide students with the tools for exploring a new dataset, with an eye towards identifying patterns, trends, and outliers. Students will gain experience with a range of graphical representations, and will learn how to select appropriate representations for different scenarios. Methods of dimensionality reduction such as PCA and t-SNE will be covered, with attention to both the mathematical underpinnings of these methods as well as their practical use. In addition to building a graphical representation toolkit, students will also be introduced to methods of non-parametric inference commonly used in real-world data applications. (3 credits, Spring only)

### DTSC 330: Big data and databases

Data science requires interaction with large datasets spread across a variety of infrastructures. We will learn about databases in practice as well as tools for computation with big data including SQL databases, NoSQL databases, and tools such as Spark. (3 credits, Spring only)

### DTSC 481: Data Science Capstone Project

This course offers students the opportunity to use their data science skills to study problems that arise in real-world settings through an individual or group project. Students will explore solution strategies, implement a strategy, interpret their findings, and communicate their results in written form and/or orally. (3 credits, Spring only)

_{Additional Coursework}

The B.S. major must also adhere the college core for the Bachelor of Science Department of Mathematics and Computer