Mathematics
Galileo said that “mathematics is the language with which God has written the universe.” Our mathematics courses are fundamentally intended to develop and sharpen your skills in this language; with mathematical understanding comes an increased awareness of and appreciation for the natural order behind God’s creation.
Mathematics has long been regarded as a natural component of a liberal arts education because of its strongly analytical, problem-solving emphasis. Recently, there has been increased recognition of the importance of mathematics in the job market; in a technological society, doors are often closed to job-seekers with a deficient mathematics background. If you desire mathematical preparation for a career in industry, scientific research, engineering or education, you’re well-advised to consider a math major or many courses in mathematics. If you’re interested in engineering, you can take a pre-engineering program of two- or three year duration at Northwestern before transferring to an engineering school to complete your training.
Requirements:
Mathematics electives: 9 credits (excluding 090, 105, 107, 109, 111, 117 and 308)
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 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 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.
Choose one course:
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 375 - 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 411 - College Geometry
(3 credits, alternate years, consult department) A study of topics in Euclidean geometry as well as axiomatic systems, non- Euclidean geometry, and projective geometry. Prerequisite: C- or better in MAT180WI or permission of instructor.
Choose one course:
MAT 312 - Differential Equations
(3 credits) A study of the elementary theory, methods of solution, and applications of differential equations, which may include topics such as first order ordinary differential equations, linear equations with constant coefficients, series solutions, variation of parameters, Laplace Transforms, linear systems, partial differential equations, and Fourier Series. Prerequisite: C- or better in MAT211 or permission of department chair.
PHY 212 - Classical Physics II
(4 credits) This is the second in a two-course calculus-based sequence. Topics include electricity, magnetism, electromagnetic waves, electromagnetism, and optics. Prerequisite: successful completion of PHY211SN with a grade of C- or better.
Note: There is a laboratory component to this course.
PHY 270 - Classical Dynamics
No course description available.
Choose one course:
MAT 412 - Real Analysis
(3 credits, alternate years, consult department) A study of real-value functions including such topics as continuity, sequences and series, differentiation and integration. Students will also be introduced to the concept of a general metric space. Prerequisite: C- or better in MAT180WI and MAT211, or permission of instructor.
MAT 419 - Introduction to Abstract Algebra
(3 credits, alternate years, consult department) A study of groups, normal groups and factor groups, Cayley's Theorem, rings, ideals, homo-morphisms, integral domains, fields, polynomial rings, field extensions and zeros of polynomials. Prerequisite: C- or better in MAT317 or permission of instructor.
Cognate requirements:
Choose one course:
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 171QR - Computer Science I
(4 credits) (NWCore option under Quantitative Reasoning) This is the first in a two-semester sequence of courses that introduces students to fundamental aspects of the field of computing; focusing on problem-solving, software design concepts and their realization as computer programs. Topics include procedural abstraction, control structures, iteration, data types and their representation. An introduction to a high-level language, for the purpose of gaining mastery of these principles, will be provided in lectures and hands-on laboratory experiences. Prerequisite: ACT math score of 20 or above (SAT 510 or above).
Choose one course:
CHE 433WIx - Introductory Physical Chemistry
(4 credits; alternate years, consult department) (Writing intensive) An introductory course in chemical
thermodynamics, quantum chemistry and chemical kinetics. Prerequisites: MAT112QR; and CHE112 or PHY212. Cross-referenced in physics.
Note: Three lectures and one three-hour laboratory period per week.
PHY 211SN - Classical Physics I
(4 credits) (NWCore option under Science and the Natural World) This is the first in a two-course calculus-based sequence. Topics include kinematics, Newtonian mechanics, energy, momentum, gravity, atomic physics, thermodynamics, and simple harmonic oscillations. Prerequisite: C- or higher in MAT112QR or consent of the department chair.
Note: There is a laboratory component to this course.
Total credits required: 46-48
Notes:
Students may choose to count CHE433, Introductory Physical Chemistry and/or CHE436, Intermediate Physical Chemistry toward mathematics electives in the mathematics major. CHE433, Introductory Physical Chemistry may not count as both the cognate and a mathematics elective.
Students pursuing secondary education certification in mathematics need to include MAT411, MAT419, and either MAT316 or MAT116QR.
