# Mathematics Courses at Hamline University

## MATH 1130 - Fundamental Concepts of Mathematics

Goals: To gain an understanding of how the language of mathematics is used in problem solving. This course is especially appropriate for prospective elementary teachers.

Content: Precise formulation of problems, symbolization, strategies for solution of mathematical problems, introduction to various number systems and to mathematical logic.

Credits: 4 credits

## MATH 1150 - Precalculus

Goals: To gain an understanding of how the language of mathematics is used in problem solving. This course is especially appropriate for prospective elementary teachers.

Content: Precise formulation of problems, symbolization, strategies for solution of mathematical problems, introduction to various number systems and to mathematical logic.

Credits: 4 credits

## MATH 1170 - Calculus I

Goals: To learn how to use the calculus of one variable and the fundamental concepts of the calculus.

Content: Limits, continuity, derivatives and integrals of functions of one variable. Applications are taken mostly from the physical sciences.

Prerequisite: Twelfth-grade high school mathematics with at least B grades or consent of instructor.

Credits: 4 credits

## MATH 1180 - Calculus II

Goals: To learn how to use the calculus of one variable and the fundamental concepts of the calculus.

Content: Integrals of functions of one variable, sequences and series. Applications are taken mostly from the physical sciences.

Prerequisite: MATH 1170 or consent of instructor.

Credits: 4 credits

## MATH 1200 - Applied Modeling and Statistics

Goals: To provide students with a computationally intensive introduction to statistics emphasizing multivariate modeling.

Content: Descriptive statistics, multivariate regression, single and multi-way analysis of variance, logistic regression, elementary probability, hypothesis testing and experimental design.

Prerequisite: None, though a firm grasp of pre-calculus mathematics is expected

Credit will not be given for both MATH 1200 and PSY 1340 or MATH 1200 and MGMT 1310.

Credits: 4 credits

## MATH 3320 - Multivariable and Vector Calculus

Goals: To extend concepts of calculus in two variables to the calculus of several variables.

Content: Vector calculus, partial and total differentiation, maximum/minimum problems, multiple integration, line and surface integrals, vector and scalar fields, theorems of Green, Gauss, and Stokes.

Taught: Fall term.

Prerequisite: MATH 1180.

Credits: 4 credits

## MATH 3330 - Linear Algebra

Goals: To gain an appreciation for how abstract structures are used to solve theoretical and practical problems.

Content: Systems of linear equations, matrices, determinants, vector spaces and bases, transformations, eigenvectors, introduction to linear differential equations.

Taught: Fall term.

Prerequisite: MATH 1180 or consent of instructor.

Credits: 4 credits

## MATH 3440 - Discrete Mathematics

Goals: To introduce the concept of the discrete as well as techniques used in higher non-continuous mathematics, providing the necessary background material required by computer scientists for algorithm analysis.

Content: Sets and numeration, combinatorics, logic, algorithms, recursion, generating functions, graphs, and trees.

Taught: Alternate years, spring term.

Prerequisite: MATH 1170.

Credits: 4 credits

## MATH 3550 - Foundations of Mathematics

Goals: To study mathematics as a logico-deductive system and to analyze those concepts and techniques that underlie all of mathematics.

Content: Logic, proof construction, sets, relations, functions, mathematical induction, arguments involving infinite sets, number systems, axiomatics.

Taught: Spring term.

Prerequisite: MATH 1180.

Credits: 4 credits

## MATH 3560 - Modern Geometry

Goals: To introduce to the concept of model building in mathematics from both a synthetic and an axiomatic point of view.

Content: Various geometries are studied with attention paid to what geometry is. Hilbert’s axiom system for Euclidean geometry, hyperbolic geometry, and transformations.

Taught: Alternate years, spring term.

Prerequisite: MATH 1170.

Credits: 4 credits

## MATH 3720 - Introduction to Applied Mathematics

Goals: To introduce techniques and methods of mathematics especially appropriate to the physical sciences.

Content: Introductory ordinary differential equations, linear partial differential equations, emphasizing separation of variables, Fourier series, special functions.

Taught: Spring term.

Prerequisite: MATH 3320 and PHYS 1240 or consent of instructor.

Credits: 4 credits

## MATH 3720- LAB: Introduction to Applied Mathematics

This lab must be taken concurrently with the MATH 3720 lecture.

The lab itself has zero credit value.

## MATH 3810 - PROBABILITY

Goals: An introduction to probability, to provide students with a computationally intensive introduction to statistics emphasizing multivariate modeling.

Content: Sample spaces, probability distributions and densities, mathematical expectation, variance, moment generating functions, random variables and functions of random variables

Taught: Fall term.

Prerequisites: MATH 1180

Credits: 4 credits

## MATH 3890 - Algebra 1

Goals: An introduction to algebraic structures. This course will develop the
properties of integers, especially the properties of prime numbers, starting
from the Peano Axioms and show how the structure of prime numbers is reflected
in the structure of the ring of integers modulo n.

Content: Equivalence relations. Peano Axioms. Fundamental Theorem of Arithmetic. Diophantine equations. Prime numbers. Gaussian integers. The group of integers modulo n. Fundamental Theorem of Finite Cyclic Groups.

While not a prerequisite for MATH 5890, this course is the first in a two semester sequence, along with MATH 5980, in modern algebra.

Taught: Fall term.

Prerequisite: MATH 1180.

Credits: 4 credits

## MATH 3910 - Analysis 1

Goals: An introduction to complex variables, including a study of the topology of the plane required.

Content: Properties of complex numbers and analytic functions of one complex variable. Power series. Cauchy’s theorem, and applications to integration. Applications.

While not a prerequisite for MATH 5910, this course is the first in a two semester sequence, along with MATH 5910, in modern analysis.

Taught: Alternate years, spring term.

Prerequisite: MATH 1180.

Credits: 4 credits

## MATH 5720 - Ordinary Differential Equations with Numerical Methods

Goals: To learn to determine both the qualitative and quantitative properties of those functions which satisfy ordinary differential equations, using both analytic and numerical techniques.

Content: Analytic methods of solution, numeric methods of solution, linear differential equations, series solutions, the Laplace transform, systems of differential equations, initial and boundary value problems, existence theory and applications.

Taught: Alternate years, fall term.

Prerequisite: MATH 3320.

Credits: 4 credits

## MATH 5810 - Mathematical Statistics

Goals: To gain an understanding of both probability and statistics as not merely collecting and organizing data but as the science of basing inferences on observed data and making decisions in the face of uncertainty. The student will be prepared to take the preliminary actuarial examination in probability and statistics.

Content: Probability distributions, mathematical expectation, random variables, point and interval estimation, hypothesis testing, regression and correlation, analysis of variance.

Taught: Alternate years, fall term.

Prerequisite: MATH 3810 or consent of instructor

Credits: 4 credits

## MATH 5850 - Numerical Analysis

Crosslisted

(Also listed as CSCI 5850.)

Goals: To introduce the methods of modern computation as used in solving problems with the aid of a computer using various algorithms.

Content: Algorithms for the solution of equations in one variable, interpolation and polynomial approximation, numerical differentiation and integration, initial-value problems for differential equations, solution of linear systems by direct or iterative techniques and various methods of approximation.

Taught: Alternate years, fall term.

Prerequisite: MATH 3320.

Credits: 4 credits

## MATH 5890 - Algebra II

Goals: To continue the study of algebraic structures begun in MATH 3330 with the goal of seeing how the building of these mathematical models yields powerful tools to understand the global nature of mathematics.

Content: Development of the elementary concepts of groups, rings, and fields.

Taught: Spring term.

Prerequisites: MATH 3330 and MATH 3550.

Credits: 4 credits

## MATH 5910 - Analysis II

Goals: To learn the language, fundamental concepts, and standard theorems of analysis. To also learn how to reason deductively from explicit assumptions and definitions in mathematical analysis, thus developing analytic techniques for attacking problems that arise in applied mathematics. Recommended for students considering graduate school in mathematics.

Content: An introduction to real analysis with emphasis on proofs of theorems and on problem solving. Topics include properties of the real number system, functions, sequences, limits and continuity, differentiation, integration, and infinite series including sequences and series of functions.

Taught: Alternate years, fall term.

Prerequisites: MATH 3330 and MATH 3550.

Credits: 4 credits

## MATH 5920 - Junior Seminar

Goals: The student will be introduced to ideas and issues that are outside of the regular undergraduate curriculum, studying how mathematics is used in academia and industry.

Content: Reviews of current research and projects of various mathematicians: senior math majors, guest lecturers, and department staff. Student presentations of topics from internships, independent studies, or honors projects.

Credits: 0.5 credit per term

## MATH 5930 - Senior Seminar

Goals: The student will be introduced to ideas and issues that are outside of the regular undergraduate curriculum, studying how mathematics is used in academia and industry.

Content: Reviews of current research and projects of various mathematicians: senior math majors, guest lecturers, and department staff. Student presentations of topics from internships, independent studies, or honors projects.

Credits: 0.5 credit per term

## MATH 5950 - Topics in Advanced Mathematics

Goals: To synthesize previous work in the various areas of mathematics with the goal of putting the areas in a historical perspective and of relating them to the question of what makes up mathematics.

Content: The content of the seminar varies from year to year depending on the instructor. Attention is paid to the history of mathematics and to filling gaps in the spectrum of mathematics presented at the undergraduate level.

Taught: Spring term.

Prerequisite: MATH 3550.

Credits: 4 credits