Data Science and Statistics
Mathematics has long been regarded as a natural component of a liberal arts education because of its strongly analytical, problem-solving emphasis. More recently, our technological and data-driven society has brought increased recognition of the importance of mathematical and statistical reasoning, making a mathematics, statistics or actuarial science major (or a math, math teaching or stats minor) an excellent choice for anyone considering a career in industry, scientific research, data analysis, predictive modeling, engineering or education.
At Northwestern, we believe that the utility of mathematics for those and other fields follows from its power as a universal language. Mathematics and statistics courses offered here are designed to develop and sharpen your skills in this language in part because increased mathematical understanding can bring an increased awareness of and appreciation for the order behind God’s creation and for the attributes of God reflected in creation.
We also believe that mathematics is one and eternal, shining forth from the mind of God. That we can comprehend some part of mathematics is evidence that human beings are created in the image of God. That the one and eternal God has enabled our mathematical discovery is an excellent reason to deepen our understanding of mathematics.
Requirements:
MAT 112QR - Calculus I
(4 credits) (NWCore option under Quantitative Reasoning) This course is a study of functions, limits, derivatives and integrals with a strong emphasis on both theory and applications. Prerequisites: C- or higher in MAT109, or an ACT math score of at least 24 (SAT 570 or above), or permission of mathematics department chair. Note: Meets four times per week.
MAT 180WI - Logic and Discrete Mathematics
(3 credits) (Writing intensive) An introduction to the language and logic of mathematical proof via topics in discrete mathematics. Topics will include logic, elementary number theory, basic set theory and methods of mathematical proof (direct proof, indirect proof, induction). Prerequisite: C- or better in MAT 112QR or permission of instructor.Note: Other topics will be chosen from counting, functions, relations, recursion and graph theory.
MAT 211 - Calculus II
(4 credits) A study of transcendental functions, techniques of integration, improper integration, sequences, series, polar coordinates and conic sections. Prerequisite: C- or better in MAT112QR or permission of instructor.Note: Meets four times per week.
MAT 212 - Calculus III
(4 credits) A study of the cylindrical and spherical coordinate systems, vectors in two dimensions and three dimensions, vector valued functions, functions of several variables, multiple integration, and vector calculus. Prerequisite: C- or better in MAT211 or permission of instructor.Note: Meets four days per week.
MAT 270 - Introduction to Data Science
(2 credits; alternate years, consult department) This course builds on and extends student skills in gaining insights fromdata with special emphasis on analysis and interpretation. Prerequisites: CSC170 and MAT116QR.
MAT 316 - Probability and Statistics I
(3 credits, alternate years, consult department) A post-calculus course in probability and statistics, which develops the theory of discrete and continuous distributions, expected value, random variables and inferential statistics. Prerequisites: C- or better in MAT116QR or 117QR, 208QR, and MAT112QR or permission of instructor.
MAT 317 - Linear Algebra
(3 credits) A study of the algebra of matrices and vector spaces including matrix operations, systems of equations, determinants, properties of real vector spaces, eigenvalues and eigenvectors. Prerequisite: C- or better in MAT112QR and MAT180 or permission of instructor.
MAT 330 - Data Validation
(3 credits; alternate years, consult department) A course building student skills in working with large data sets gathered from real-world studies and experiments. Students will learn and experience best practices for data-type, range, constraint, code, cross-reference, structured, and textual validation. Prerequisites: CSC170 and one of the following: MAT116QR, MAT117QR, MAT208QR or PSY215.
MAT 375x - Econometrics with Regression Analysis
(4 credits) This course, which is required for finance, economics, and actuarial science majors, is designed to introduce students to the fundamentals of econometric analysis. To this end, the primary focus is on simple and multiple linear regressions using cross-sectional data and time series regressions. We will also discuss highly useful extensions including regression with binary dependent variables, and regression analysis using panel data if time. The course will put a heavy emphasis on empirical applications; econometric theory will be discussed where necessary but will not be the central focus. Instead, we focus on estimating regression models using statistical packages such as R, SPSS, or Stata, and on interpreting the results. Both estimation and interpretation are highly marketable skills. The coverage of this course will be sufficient for SVEE Applied Statistics (SOA) and useful for CFA exams. More broadly, what you learn from this course will be valuable for a career in consulting, banking, insurance, and other related fields. Prerequisite: C- or better in MAT112QR and in MAT116QR or MAT117QR.Cross-Referenced: Cross-referenced in economics.
MAT 416 - Probability and Statistics II
(3 credits, alternate years, consult department) A continuation of Probability and Statistics I. Emphasis will be placed on functions of random variables and sampling distributions. Prerequisite: MAT316.
MAT 445 - Statistical Design
(3 credits; alternate years, consult department) A course focusing on the theory and objectives critical to the design and implementation of sound statistical experiments and surveys, including survey and experimental methods. Emphasis on sampling techniques, instrument design, reliability and validity. Prerequisite: CSC170QR, MAT112QR and MAT116QR or MAT117QR.
MAT 450SR - Mathematical Minds
(3 credits) This course will provide you with a survey of some of the fascinating and critical ideas in mathematics, including historical proofs of some results which are familiar to you through your previous mathematical study as well as some results which will be new to you. We will also spend a significant amount of time discussing connections between mathematics and the Christian faith, and we'll take a look into the background of the mathematically and scientifically significant number 0, which has had its own theological issues. And you'll explore the contributions of the various parts of your college experience to the goals of the NWCore program and your progress in establishing personal commitments and a sense of vocation. Prerequisites: C- or better in MAT211 or permission of instructor.
Cognate requirements:
CSC 170 - Statistical Programming
(4 credits) In today's data-driven world, statistical literacy and data analysis are increasingly important skills. This course introduces students to the fundamental aspects of programming, such as data types, procedural abstraction, control structures, and iteration, with a focus on the application of these concepts to statistics and data analysis. Topics will include the programmatic implementation of summary statistics, correlation, linear modeling, and clustering. A statistics-focused language, such as R, is covered in-depth for the purpose of gaining mastery of these principles. Prerequisites: Math ACT subscore of 20 or above (SAT 510 or above)
CSC 172WI - Computer Science II
(4 credits) (Writing intensive) This course moves students into the domain of software design, introducing principles that are necessary for solving large problems. Here, the classical software design process serves as a basis for treating such topics as abstract data types, specifications, complexity analysis and file organization. Basic data structures and transformations are introduced as representative of the fundamental tools that are used to aid in this process. A high-level language will be used for the purpose of gaining mastery of these principles through lectures and independent hands-on laboratory experiences.Prerequisite: CSC171QR.
CSC 291 - Database Management Systems
(4 credits; alternate years, consult department) This course examines database concepts, theory, design and management. Emphasis will be on the relational model. Topics will also include normalization, query languages, database recovery and security aspects. This course will include experience with a relational database system and programming database access into computer applications via a high-level programming language. Prerequisite: CSC171QR.
CSC 310 - Data Visualization
(4 credits; alternate years, consult department) Data visualization provides insight into unfamiliar data sets, identifies issues in statistical models, and helps effectively communicate results. This course will focus on all of these aspects, starting with exploratory and evaluative techniques and progressing to creating professional, publication-quality visualizations. The classroom experience will alternate between discussion of best practices and case studies and hands-on learning of industry-standard visualization programming librarie, and culminate with a comprehensive visualization project. Prerequisites: CSC170 or CSC171QR.
CSC 341 - Data Mining and Machine Learning
(4 credits; alternate years, consult department ) Data mining is the practice of analyzing large datasets using automated computational methods to discover patterns and generate knowledge that would not be detected by human inspection alone. Machine learning is the use of algorithms and statistical models to analyze and draw inferences from the patterns found in large data sets. Other closely related terms include artificial intelligence, statistical learning, data science, and predictive data analytics. This course will present the basic theories and foundational mathematics behind machine learning. Students will implement these concepts using an appropriate programming language and develop their own machine learning project. Specific attention will be paid to the ethical and social issues arising from the use of this technology. Prerequisite: CSC172WI.
CSC 351 - Data Structures
(4 credits; alternate years, consult department) This course deals with data structures and their algorithms. Emphasis is given to good data abstraction and efficiency. The data structures covered include arrays, linked lists, trees, graphs and strings. Other topics covered may include design patterns, analysis of algorithms, and complexity classes. Programming is done in an object-oriented language. Prerequisite: CSC172WI.
