# Math Courses | Northwestern College in Iowa

MAT090

– Basic Algebra

This course covers basic concepts of numbers (addition, subtraction,

multiplication and division in the integers, rational numbers and real

numbers), basic properties of exponents, linear equations in two

variables and their applications in problem solving, inequalities, the

use of formulas and an introduction to the rectangular coordinate system

and graphing. Counts toward full-time student status but is not included

in grade point averages. Credit attempted in Basic Algebra does not count

toward graduation. Does not count toward a math major or minor. Does not

fulfill the math requirement or any graduation requirement. (2 credits)

MAT105QR

– Topics in Contemporary Mathematics

(3 credits)(NWCore option under Quantitative Reasoning) This course will

explore a variety of mathematical topics arising in

today's technological society and include a historical component of

mathematical developments. Possible topics include exposure to both

symbolic and verbal logic, set notation, statistics, and finance. A

primary goal will be to introduce, view, and gain a deeper appreciation

for a broad panorama of mathematical fields and how each field has been

utilized to help shape today's culture.

Prerequisite: C- or better in MAT090 or an ACT math score of 20 or above

(SAT 510 or above), or a passing score on basic algebra placement exam.

MAT107QR

– Mathematics for Elementary Teachers

MAT 107 is a study of the topics necessary and helpful for competent and

enthusiastic teaching of mathematics in the elementary school. The course

topics include numbers and operations, number bases, fractions, decimals,

ratio, measurement, geometry, number theory, data analysis, and probability.

The goal of the course is to develop conceptual understanding of these

topics through the 5 process standards proposed by the National Council of

Teachers of Mathematics: problem solving, reasoning and proof,

communication, connections, and representations as well as the Standards for

Mathematical Content and Practice from the Common Core State Standards for

Mathematics. While not used exclusively, this course emphasizes

inquiry-based activities that will help you to analyze and understand

children's ways of thinking, effective communication of mathematical ideas,

and use of appropriate manipulatives and technology for teaching. Course

enrollment is limited to Education majors and does not count toward a math

major or math minor. Prerequisite: A grade of C- or better in MAT 090, ACT math score of at least

20 (SAT math 510), or a passing score on the MAT 090 placement exam. (3

credits) (NWCore option under Quantitative Reasoning)

MAT109QR

– College Algebra

This course covers algebraic material prerequisite to middle school

mathematics teaching and to the study of calculus. Topics include a thorough

study of functions (linear, polynomial, exponential, and logarithmic, as

well as combinations of functions through addition/subtraction,

multiplication/division, and composition), inverse functions, solving

equations and systems of equations, matrices, and conic sections. Prerequisite: C- or better in MAT090 or an ACT math score of 20 or above

(SAT 510 or above). (3 credits) (NWCore option under Quantitative Reasoning)

MAT111QR

– Calculus for Management, Life and Social Sciences

(3 credits)(NWCore option under Quantitative Reasoning) This course is a

study of functions, limits, derivatives and integrals

with an emphasis on techniques and applications in business, biology,

health, and social sciences.

Note: Does not count toward a math major or minor.

Prerequisites: C- or higher in MAT109, or an ACT math score of at least 22

(SAT 550 or above), or permission of mathematics department chair.

MAT112QR

– 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.

MAT116QR

– Statistics for the Natural and Social Sciences

(3 credits)(NWCore option under Quantitative Reasoning) This course is

designed to introduce topics in probability and statistics

with an emphasis on problems in the sciences. We will study discrete and

continuous distributions, estimation and hypothesis testing, p-values,

correlation, and simple linear regression. There will be three main

sections in this course, examining descriptive statistics (the nature of

data and how to summarize it), basic probability concepts (the

mathematical study of uncertainty), and inferential statistics (making

claims or decisions based on one or more sets of data).

Note: Students may receive credit for only one course among MAT

116QR, MAT 117QR and MAT 208.

Prerequisites: C- or better in MAT090, an ACT math score of 20 or above

(SAT 510 or above), a passing score on the basic algebra placement exam,

or permission of instructor.

MAT117QR

– Applied Statistics for Management

(3 credits)(NWCore option under Quantitative Reasoning) The course is

designed to study statistical methodology commonly used in

business including descriptive statistics (the nature of data and how to

summarize it), basic probability concepts, and inferential statistics

(making claims or decisions from one or more sets of data using

confidence intervals and multiple types of hypothesis testing).

Note: Students may receive credit for only one course among MAT

116QR, MAT 117QR and MAT 208.

Prerequisites: C- or better in MAT090, an ACT math score of 20 or above

(SAT 510 or above), a passing score on the basic algebra placement exam,

or permission of instructor.

MAT127

– Patterns, Functions and Algebra for Elementary Teachers

MAT127 is designed to help you understand and teach the aspects of algebra

that are highly relevant to elementary and middle school classrooms.

Throughout the course, topics are explored through rich problems and

investigations, enabling you to deepen your conceptual understanding of

algebraic concepts and to enhance your pedagogical practices. Course

discussions, activities, projects, and explorations will focus on the

following topics: Problem Solving, Solving Equations, Patterns & Sequences, Representing Functional

Relationships, Quadratic Functions, Exponential Functions, Properties of Numbers and

Operations, Algebraic Proof. Prerequisites: C- or better in MAT090 or ACT

math score of 20 or above (SAT 510 or above), or passing score on the MAT090

placement exam. (3 credits) Note: This course is limited to elementary

education majors only. Does not count toward a math major or minor.

MAT180WI

– 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.

MAT208QR

– Biostatistics

(4 credits)(NWCore option under Quantitative Reasoning) This course is a study of statistical methodology commonly used in the

biological and health sciences. We will start with examining basic

descriptive methods in statistics. We will then introduce the foundational

concepts in probability. After these topics are explored, we will spend the

remainder of the course looking at the uses and interpretation of

statistics. Topics will include confidence intervals and hypothesis tests

involving one or two samples, correlation and regression, contingency

tables, and ANOVA.

Note: Meets four times per week. Students may receive credit for only one

course among MAT 116QR, MAT 117QR and MAT 208QR.

Prerequisite: C- or better in MAT090, an ACT math score of 20 or above (SAT

510 or above), or a passing score on MAT090 placement exam.

MAT211

– 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)

MAT212

– 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)

MAT308

– Methods of Teaching Secondary School Mathematics

(3 credits, alternate years, consult department) Content, techniques and

materials for teaching mathematics at the

secondary or junior high level. This course

requires a

30-hour practicum and is required of each candidate seeking an

endorsement in this content area.

Notes: Does not count toward a major or minor in mathematics. Students must

earn a "C" or better in the special methods course in order

to fulfill program requirements for secondary licensure.

Prerequisite: Junior or senior class standing.

MAT312

– 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)

MAT316

– 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)

MAT317

– 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)

MAT325

– Topics in the History of Mathematics

MAT330

– Data Validation

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: CSC 170 and one of the

following: MAT116QR, MAT117QR, MAT208QR or PSY 215. (3 credits; alternate years, consult

department)

MAT375

– 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.

MAT385

– Advanced Regression Analysis

A course building on simple and multiple linear regression analysis to

introduce multivariate analysis, logistic regression, moderation, matric

formulation, residual analysis, transformations, regression diagnostics,

multicollinearity, and variable selection techniques. Prerequisite: MAT375. (3 credits; alternate years, consult

department)

MAT398

– Directed Study

MAT411

– 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)

MAT412

– 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)

MAT416

– Probability and Statistics II

A continuation of Probability and Statistics I. Emphasis will be placed on functions of random variables and sampling distributions.Prerequisite: MAT316.(3 credits, alternate years, consult department)

MAT417

– Internship

(2 credits may apply toward the major)

MAT419

– 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)

MAT420

– Actuarial Exam Review

This course is a comprehensive review of all materials for SOA/CAS exams. The course is tailored to the specific exam the student is planning on taking.Prerequisite: permission of chair of department.(1 credit)

MAT425

– Advanced Topics in Mathematics

This course will explore in more depth some of the mathematics that has been introduced in earlier courses. Topics will vary depending on the interests of students and faculty, but include complex analysis, graph theory and combinatorics, math modeling, number theory, topology, and measure theory. Prerequisites: MAT180, 212, and 317; or permission of instructor. (3 credits, offered as needed)

MAT430

– Actuarial Modeling: Life Contingent Risk Models

This course is an introduction to the study of contingent payment models. Topics include: economics of insurance, individual risk models, survival distributions and life tables, benefit reserves, multiple life functions, multiple decrement models and introductory loss models.Prerequisite: MAT416.(3 credits, alternate years, consult department)

MAT431

– Actuarial Modeling: Loss Models

This course concentrates on loss models. Topics include: frequency and

severity, aggregate loss models, discrete and continuous time ruin models,

construction of empirical models, parameter estimation, and model selection.

Prerequisite: MAT316, with co-requisite MAT416. (3 credits; alternate years, consult department)

MAT435

– Bayesian Analysis

An introduction to Bayesian statistical modeling and inference and related

computational strategies and algorithms, including posterior and predictive

inference; Bayesian models in applications; methods of prior elicitation;

and computation, visualization, and analysis of real-world data. Prerequisites: MAT 116QR and MAT 180WI. (3 credits;

alternate years, consult department)

MAT445

– Statistical Design

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: MAT 375. (3 credits; alternate years, consult

department)

MAT450SR

– 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)