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.
Note: Meets four times per week.
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.
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).
Note: Other topics will be chosen from counting, functions, relations,
recursion and graph theory.
Prerequisite: C- or better in MAT 112QR or permission of instructor.
MAT 211 - Calculus II
A study of transcendental functions, techniques of integration, improper integration, sequences, series, polar coordinates and conic sections.Prerequisite: C- or better in MAT112 or permission of instructor.(4 credits)
MAT 212 - Calculus III
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.(4 credits)
MAT 317 - Linear Algebra
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 180 or permission of instructor.(3 credits)
MAT 450SR - Mathematical Minds
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 IGE program and your progress in
establishing personal commitments and a sense of vocation. Prerequisites: grade of C- or better in MAT211 or permission of
instructor. (2 credits)
Choose one course:
MAT 316 - Probability and Statistics I
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 MAT116 or 117, 180, 211 or permission of instructor.(3 credits, alternate years, consult department)
MAT 375 - Econometrics with Regression Analysis
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 117QR. (4 credits) Cross-referenced in economics.
MAT 411 - College Geometry
A study of topics in Euclidean geometry as well as axiomatic systems, non- Euclidean geometry, and projective geometry.Prerequisite: C- or better in MAT180 or permission of instructor.(3 credits, alternate years, consult department)
Choose one course:
MAT 312 - Differential Equations
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.(3 credits)
PHY 212 - Classical Physics II
A continuation of Classical Physics I. Topics will include simple harmonic oscillation, mechanical and electromagnetic waves, and electromagnetism.Prerequisite: successful completion of PHY211 with a grade of C- or better.(4 credits)
PHY 270 - Classical Dynamics
Choose one course:
MAT 412 - Real Analysis
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 211, or permission of instructor.(3 credits, alternate years, consult department)
MAT 419 - Introduction to Abstract Algebra
A study of groups, normal groups and factor groups, Cayley's Theorem, rings, ideals, homomorphisms, integral domains, fields, polynomial rings, field extensions and zeros of polynomials.Prerequisite: C- or better in MAT317 or permission of instructor.(3 credits, alternate years, consult department)
Cognate requirements:
Choose one course:
CSC 170 - Statistical Programming
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: C- or better in MAT 090 or 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: C- or better in MAT090, an ACT math score of 20 or above
(SAT 510 or above), or a passing score on the MAT090 placement exam.
Choose one course:
CHE 433WIx - Introductory Physical Chemistry
An introductory course in chemical thermodynamics, quantum chemistry and
chemical kinetics. Note: Three lectures and one three-hour laboratory
period per week.
Prerequisites: MAT112QR; and CHE112 or PHY212. (4 credits;
alternate years, consult department)(Writing intensive) Cross-referenced in physics.
PHY 211SN - Classical Physics I
(4 credits)(NWCore option under Science and the Natural World) Though all
students are welcome in this calculus-based, IGE physics course, this is the
first of a two course sequence designed for math, science, and engineering
majors and others who have taken or are taking calculus and intend to apply
to medical or graduate school. This course includes the following topics:
kinematics, Newtonian mechanics, energy, momentum, gravity, oscillations,
and thermodynamics.
Prerequisite: C- or higher in MAT 112, or consent of the department chair.
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.
