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Mathematics B.A.

Division of Science & Mathematics - Adm
Division of Science and Mathematics
  • Program Type: Baccalaureate
  • Requirements for this program are current for Fall 2015
  • Required credits to graduate with this degree: 120
  • Required credits within the major: 52
  • Degree: Bachelor of Arts
Objectives--The mission of the discipline is to advance knowledge of mathematics by teaching mathematics and its processes, by research in mathematics and mathematical pedagogy, and by dissemination of this knowledge to students and the community we serve. Historically, the study of mathematics has been central to a liberal arts education. The mathematics curriculum serves as an integral part of students' active pursuit of a liberal arts education. The mathematics program serves students who major or minor in mathematics, seek secondary mathematics teaching licensure, major or minor in programs that require a mathematical background, or wish to fulfill components of a general education. The mathematics curriculum is designed to help students develop competence in problem-solving, mathematical techniques and methods; to sharpen students' mathematical intuition and abstract reasoning, as well as their quantitative literacy. The curriculum is also designed to encourage and stimulate the type of independent and critical thinking required for research beyond the confines of the textbook. It provide students with the basic knowledge and skills to make mathematical contributions to modern society. The mathematics program enables students to do in-depth and independent mathematics-related research projects that require students to integrate their mathematical knowledge from different areas, and to enhance their communication skills by way of written reports and oral presentations. The program seeks to enable students to observe and communicate how the development of mathematics has been part of historical and current cultural and scientific developments. The curriculum prepares students to enter graduate school, pursue careers in applied mathematics, or teach mathematics.
Program Delivery
This program is available:
  • via classroom (the majority of instruction is face-to-face)
Admission Requirements
For information about University of Minnesota admission requirements, visit the Office of Admissions website.
General Requirements
All students are required to complete general University and college requirements. For more information, see the general education requirements.
Program Requirements
Students are required to take 2 semester(s) of any second language.
A minimum GPA of 2.00 is required in the major to graduate. The GPA includes all, and only, University of Minnesota coursework. Grades of "F" are included in GPA calculation until they are replaced. Courses may not be taken S-N unless offered S-N only. Up to 5 credits of coursework with a grade of D or D+ may be used to meet the major requirements if offset by an equivalent number of credits of B- or above in courses at or above 2xxx. Exceptions to requirements may be granted on an individual basis, after consulting with the math faculty. Majors should begin with MATH 1012 - PreCalculus I or MATH 1013 - PreCalculus II or MATH 1101 - Calculus I. Students with questions about placement are encouraged to discuss them with members of the mathematics faculty. Recommended electives for students planning to pursue graduate work in pure mathematics: MATH 4201 - Complex Analysis MATH 4211 - Real Analysis MATH 4221 - Topology MATH 4231 - Abstract Algebra II MATH 4241 - Number Theory MATH 4252 - Differential Geometry MATH 4253 - Combinatorics Recommended electives for students planning to work or pursue graduate work in applied mathematics or related fields: MATH 2401 - Differential Equations MATH 3401 - Operations Research MATH 3411 - Discrete and Combinatorial Mathematics MATH 4401 - Numerical Methods With Applications in Mathematical Modeling MATH 4452 - Mathematical Modeling
Residency Requirement
Students must complete a minimum of three 3xxx or higher math courses at UMM.
Required Courses
MATH 1101 - Calculus I [M/SR] (5.0 cr)
MATH 1102 - Calculus II [M/SR] (5.0 cr)
MATH 2101 - Calculus III [M/SR] (4.0 cr)
MATH 2111 - Linear Algebra [M/SR] (4.0 cr)
MATH 2202 - Mathematical Perspectives [M/SR] (4.0 cr)
MATH 3221 - Real Analysis I (4.0 cr)
MATH 3231 - Abstract Algebra I (4.0 cr)
MATH 4901 - Senior Seminar (2.0 cr)
Take 1 or more course(s) from the following:
· MATH 2401 - Differential Equations [M/SR] (4.0 cr)
· MATH 3401 - Operations Research (4.0 cr)
· MATH 3411 - Discrete and Combinatorial Mathematics (4.0 cr)
· MATH 4401 - Numerical Methods with Applications in Mathematical Modeling (4.0 cr)
· MATH 4452 - Mathematical Modeling (4.0 cr)
Take 4 or more credit(s) from the following:
· MATH 2xxx
· MATH 3xxx
· MATH 4xxx
Take 1 or more course(s) from the following:
· CSCI 1201 - Introduction to Digital Media Computation [M/SR] (4.0 cr)
· CSCI 1301 - Problem Solving and Algorithm Development [M/SR] (4.0 cr)
Take 1 or more course(s) from the following:
· STAT 2601 - Statistical Methods [M/SR] (4.0 cr)
· STAT 2611 - Mathematical Statistics [M/SR] (4.0 cr)
Mathematical Applications Course
Take 1 or more course(s) from the following:
· CHEM 3501 - Physical Chemistry I [SCI] (4.0 cr)
· CSCI 2101 - Data Structures [M/SR] (5.0 cr)
· CSCI 3402 - Computing Systems: Concepts (3.0 cr)
· CSCI 3501 - Algorithms and Computability [M/SR] (5.0 cr)
· CSCI 3601 - Software Design and Development [M/SR] (5.0 cr)
· ECON 3201 - Microeconomic Theory [SS] (4.0 cr)
· ECON 3202 - Macroeconomic Theory [SS] (4.0 cr)
· ECON 3501 - Introduction to Econometrics [M/SR] (4.0 cr)
· ECON 4111 - Mathematical Economics I (2.0 cr)
· ECON 4112 - Mathematical Economics II (2.0 cr)
· GEOL 3401 - Geophysics [SCI] (4.0 cr)
· GEOL 3501 - Hydrology [SCI] (4.0 cr)
· MATH 3501 - Applied Deterministic Modeling for Management Science (2.0 cr)
· MATH 3502 - Applied Probabilistic Modeling for Management Science (2.0 cr)
· PHIL 2101 - Introduction to Symbolic Logic [M/SR] (4.0 cr)
· PHYS 1101 - General Physics I [SCI-L] (5.0 cr)
· PHYS 1102 - General Physics II [SCI-L] (5.0 cr)
· PHYS 2101 - Modern Physics [SCI-L] (4.0 cr)
· PHYS 2401 - Optics [SCI-L] (4.0 cr)
· PHYS 3101 - Classical Mechanics [SCI] (4.0 cr)
· PHYS 4101 - Electromagnetism (4.0 cr)
· PHYS 4201 - Quantum Mechanics (4.0 cr)
· STAT 3601 - Data Analysis [M/SR] (4.0 cr)
· STAT 3611 - Multivariate Statistical Analysis [M/SR] (4.0 cr)
· STAT 4601 - Biostatistics (4.0 cr)
 
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· Division of Science and Mathematics

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· Mathematics 1
· Mathematics 2
· Mathematics 3
· Mathematics 4

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· Mathematics B.A.
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MATH 1101 - Calculus I (M/SR)
Credits: 5.0 [max 5.0]
Typically offered: Every Fall & Spring
Limits and continuity; the concepts, properties, and some techniques of differentiation, antidifferentiation, and definite integration and their connection by the Fundamental Theorem. Partial differentiation. Some applications. Students learn the basics of a computer algebra system. prereq: 1012, 1013 or placement
MATH 1102 - Calculus II (M/SR)
Credits: 5.0 [max 5.0]
Typically offered: Every Fall & Spring
Techniques of integration. Further applications involving mathematical modeling and solution of simple differential equations. Taylor's Theorem. Limits of sequences. Use and theory of convergence of power series. Students use a computer algebra system. prereq: 1101
MATH 2101 - Calculus III (M/SR)
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Multivariable and vector calculus. Three-dimensional analytic geometry; partial differentiation; multiple integration; gradient, divergence, and curl; line and surface integrals; divergence theorem; Green and Stokes theorems; applications. prereq: 1102 or instr consent
MATH 2111 - Linear Algebra (M/SR)
Credits: 4.0 [max 4.0]
Prerequisites: 1102 or #
Typically offered: Every Fall & Spring
Matrix algebra, systems of linear equations, finite dimensional vector spaces, linear transformations, determinants, inner-product spaces, characteristic values and polynomials, eigenspaces, minimal polynomials, diagonalization of matrices, related topics; applications. prereq: 1102 or instr consent
MATH 2202 - Mathematical Perspectives (M/SR)
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Introduction to the methodology and subject matter of modern mathematics. Logic, sets, functions, relations, cardinality, and induction. Introductory number theory. Roots of complex polynomials. Other selected topics. prereq: 1101
MATH 3221 - Real Analysis I
Credits: 4.0 [max 4.0]
Prerequisites: 1102, 2202 or #
Typically offered: Every Fall
Introduction to real analysis. The main topics of single-variable calculus-convergence, continuity, differentiation, and series as they are applied and extended in advanced settings with emphasis on precise statements and rigorous proofs. Structure of the real numbers, open and closed sets. Integration, metric spaces, and other topics and applications as time allows. prereq: 1102, 2202 or instr consent
MATH 3231 - Abstract Algebra I
Credits: 4.0 [max 4.0]
Prerequisites: 2111, 2202 or #
Typically offered: Every Spring
Systematic study of groups and rings, making use of linear algebra. Groups as codifying symmetry throughout mathematics and its applications. The Euclidean algorithm and its consequences, both for integers and polynomials. Other selected topics and applications. prereq: 2111, 2202 or instr consent
MATH 4901 - Senior Seminar
Credits: 2.0 [max 2.0]
Prerequisites: sr math major or #; full year course begins fall sem
Grading Basis: A-F only
Typically offered: Every Fall
This is a full-year course, required for all mathematics majors in their senior year. Students must attend year round and present one of the seminars. prereq: sr math major or instr consent; full year course begins fall sem
MATH 2401 - Differential Equations (M/SR)
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
First-order and second-order differential equations with methods of solution and applications, Laplace transforms, systems of equations, series solutions, existence and uniqueness theorems, the qualitative theory of differential equations. prereq: 1102 or instr consent
MATH 3401 - Operations Research
Credits: 4.0 [max 4.0]
Prerequisites: 1101 or higher or #
Typically offered: Every Spring
Topics include, but not limited to, linear and integer linear programming formulations, sensitivity analysis and duality, network models and applications. prereq: 1101 or higher or instr consent
MATH 3411 - Discrete and Combinatorial Mathematics
Credits: 4.0 [max 4.0]
Prerequisites: 1102 or higher or #
Typically offered: Every Fall
Propositional logic; equivalence relations; recurrence equations; structures and properties of undirected and directed graphs; applications of the aforementioned topics. prereq: 1102 or higher or instr consent
MATH 4401 - Numerical Methods with Applications in Mathematical Modeling
Credits: 4.0 [max 4.0]
Typically offered: Periodic Fall & Spring
Finite differences; interpolation; numerical integration; numerical solutions of differential, algebraic, and transcendental equations; continuous mathematical models. prereq: 2111, 2401 or instr consent
MATH 4452 - Mathematical Modeling
Credits: 4.0 [max 4.0]
Typically offered: Periodic Fall & Spring
Mathematical topics include, but are not limited to, differential and difference equations, discrete and continuous dynamical systems, predator-prey models, discrete and continuous optimization models, probabilistic models, stochastic and Poisson processes, and queuing models. Applications are drawn from different areas in the sciences and social sciences. prereq: instr consent
CSCI 1201 - Introduction to Digital Media Computation (M/SR)
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Using images, sounds, and movies to introduce problem solving, data representation, data manipulation, and programming principles including recursion. Introduction to basic ideas in hardware, software, and computing.
CSCI 1301 - Problem Solving and Algorithm Development (M/SR)
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Introduction to different problem solving approaches, major programming paradigms, hardware, software, and data representations. Study of the functional programming paradigm, concentrating on recursion and inductively-defined data structures. Simple searching and sorting algorithms.
STAT 2601 - Statistical Methods (M/SR)
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Descriptive statistics, elementary probability theory; laws of probability, random variables, discrete and continuous probability models, functions of random variables, mathematical expectation. Statistical inference; point estimation, interval estimation, tests of hypotheses. Other statistical methods; linear regression and correlation, ANOVA, nonparametric statistics, statistical quality control, use of statistical computer packages. prereq: Math 1101 or Math 1021
STAT 2611 - Mathematical Statistics (M/SR)
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Introduction to probability theory. Principles of data reduction; sufficiency principle. Point estimation; methods of finding and evaluating estimators. Hypothesis testing; methods of finding and evaluating tests. Interval estimation; methods of finding and evaluating interval estimators. Linear regression and ANOVA. prereq: Math 1101
CHEM 3501 - Physical Chemistry I (SCI)
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
The gas state. Classical thermodynamics. Phase, chemical and heterogeneous equilibria. Chemical kinetics. Kinetic theory of gases. Transport. prereq: 1102, Phys 1101, Math 1102 or instr consent
CSCI 2101 - Data Structures (M/SR)
Credits: 5.0 [max 5.0]
Typically offered: Every Fall
Introduction to data structures, including stacks, queues, trees, and graphs; implementation of abstract data types and introduction to software testing, using object-oriented techniques and reusable libraries. (4 hrs lect, 2 hrs lab) prereq: 1201 or 1301 or instr consent
CSCI 3402 - Computing Systems: Concepts
Credits: 3.0 [max 3.0]
Course Equivalencies: 02224 - CSci 3402/CSci 3401
Prerequisites: 1302 and 2101 or #
Typically offered: Every Spring
Overview of computing systems, operating systems, and networks. Sources of complexity. Fundamental abstractions such as memory, processing, and communication; memory management and data storage; threads, processes, race conditions and deadlock; and inter-process and inter-computer communication. Modularity and organization; virtualization; protection and security; performance. prereq: 1302 and 2101 or instr consent
CSCI 3501 - Algorithms and Computability (M/SR)
Credits: 5.0 [max 5.0]
Typically offered: Every Fall
Models of computation (such as Turing machines, deterministic and non-deterministic machines); approaches to the design of algorithms, determining correctness and efficiency of algorithms; complexity classes, NP-completeness, approximation algorithms. (4 hrs lect, 2 hrs lab) prereq: 1302, 2101 or instr consent
CSCI 3601 - Software Design and Development (M/SR)
Credits: 5.0 [max 5.0]
Typically offered: Every Spring
Design and implementation of medium- and large-scale software systems. Principles of organizing and managing such designs and implementations throughout their lifetime. Designing for modularity and software reuse; use of libraries. Dynamics of working in groups. Group work on a substantial software project. prereq: 1302, grade of at least C- in 2101, or instr consent
ECON 3201 - Microeconomic Theory (SS)
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Analytical approach to decision making by individual economic units in the output and input markets, under perfect and imperfect market conditions. Externalities and role of government. prereq: 1111, Math 1101 or instr consent
ECON 3202 - Macroeconomic Theory (SS)
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
The theory of national income determination; inflation, unemployment, and economic growth in alternative models of the national economy. prereq: 1112, Math 1101 or instr consent
ECON 3501 - Introduction to Econometrics (M/SR)
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Designing empirical models in economics. Simple and multiple regression analysis. Violations of classical assumptions in regression analysis. Logit and probit models; simultaneous equation models and lag models. Emphasis on application techniques to economic issues. prereq: 3201 or 3202, Stat 1601
ECON 4111 - Mathematical Economics I
Credits: 2.0 [max 2.0]
Typically offered: Periodic Fall & Spring
Application of mathematical methods to economic analysis. Mathematical formulations and solution of optimizing models pertaining to households and firms and of adjustments to disturbances. prereq: 3201, 3202 or instr consent
ECON 4112 - Mathematical Economics II
Credits: 2.0 [max 2.0]
Typically offered: Periodic Fall & Spring
Topics include linear modeling, input-output analysis and linear programming, efficiency and exchange, comparative static analysis, and dynamic microeconomic and macroeconomic models. prereq: 3201, 3202 or instr consent
GEOL 3401 - Geophysics (SCI)
Credits: 4.0 [max 4.0]
Typically offered: Fall Odd Year
Propagation of seismic waves, earthquake seismology, and the structure of the Earth; the origin and nature of the Earth's magnetic and gravitational fields; the Earth's internal production and flow of heat; composition, state, and rheology of the Earth's interior; plate tectonics and elementary geodynamics. (4 hrs lect) prereq: Math 1101, Phys 1101 or instr consent
GEOL 3501 - Hydrology (SCI)
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
An examination of the hydrological cycle; evapotranspiration and precipitation; processes of infiltration; rainfall-runoff relationships and the generation of overland flow; response of the drainage basin to storm events; flood-frequency analysis; elements of groundwater flow and evaluation of aquifer characteristics; water quality, contamination, and contaminant transport. (4 hrs lect) prereq: Math 1101 or instr consent
MATH 3501 - Applied Deterministic Modeling for Management Science
Credits: 2.0 [max 2.0]
Course Equivalencies: 00924 - Math 3501/Mgmt 3501
Prerequisites: 1101 or Stat 1601 or Stat 2601 or Stat 2611, Mgmt 2102 or #
Typically offered: Every Spring
Same as Mgmt 3501. Formulations of real-world problems as Linear Programming or Integer Linear Programming models; graphical solutions of some LP models. Linear Programming: the Simplex method, intuitive ideas behind the Simplex method. Using software to solve LP problems; interpreting optimal solutions; sensitivity analysis; duality. Network diagram representation; critical path method (CPM-PERT); transportation problem. prereq: 1101 or Stat 1601 or Stat 2601 or Stat 2611, Mgmt 2102 or instr consent
MATH 3502 - Applied Probabilistic Modeling for Management Science
Credits: 2.0 [max 2.0]
Course Equivalencies: 00925 - Math 3502/Mgmt 3502
Prerequisites: 1101 or Stat 1601 or Stat 2601 or Stat 2611, Mgmt 2102 or #
Typically offered: Every Spring
Same as Mgmt 3502. Short review of probability and statistics; mean and variance of a data set; discrete and continuous random variables (especially the exponential distribution and the Poisson distribution). Decision and game theory. Decision trees, types of decision criteria. Queueing models, birth-and-death processes; Markovian or Poisson arrivals and exponential service times; M/M/k and M/M/8 queues; Statistical Quality Control; inventory control system. prereq: 1101 or Stat 1601 or Stat 2601 or Stat 2611, Mgmt 2102 or instr consent
PHIL 2101 - Introduction to Symbolic Logic (M/SR)
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
An introduction to formal or deductive logic, including basic concepts of logical argumentation; Aristotelian logic; and symbolic translations, truth tables, and theory of deduction. Samples from political speeches, philosophical essays as well as original LSAT questions are analyzed.
PHYS 1101 - General Physics I (SCI-L)
Credits: 5.0 [max 5.0]
Typically offered: Every Spring
Vectors, kinematics, laws of motion, circular motion, work-energy theorem, conservation principles, rotational motion, gravitation, simple harmonic oscillations, wave phenomena, fluid mechanics, thermal properties of matter, kinetic theory, laws of thermodynamics. (4 hrs lect and rec, 2 hrs lab) prereq: Math 1101 or instr consent
PHYS 1102 - General Physics II (SCI-L)
Credits: 5.0 [max 5.0]
Typically offered: Every Fall
Coulomb's law, electric field, Gauss's law, electric potential, capacitance, dielectrics, current, resistance, circuits, magnetic field, Ampere's law, inductance, Faraday's law, AC circuits, Maxwell's equations, electromagnetic waves, nature of light, reflection, refraction, optical instruments, interference, diffraction. (4 hrs lect and rec, 2 hrs lab) prereq: 1101, Math 1102 or instr consent
PHYS 2101 - Modern Physics (SCI-L)
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Special relativity, quantum nature of matter and radiation, Bohr-Sommerfeld atom, atomic spectra, uncertainty principle, Schrodinger equation, hydrogen atom, electron spin, Pauli principle, and periodic table. (3 hrs lect, 3 hrs lab) prereq: 1102, Math 2401 or instr consent
PHYS 2401 - Optics (SCI-L)
Credits: 4.0 [max 4.0]
Typically offered: Spring Even Year
Light as a wave phenomenon, electromagnetic nature of light, Huygens' principle, interference, diffraction--Fraunhofer and Fresnel, polarization, dispersion, absorption and scattering. (4 hrs lect, lab TBA) prereq: 1102
PHYS 3101 - Classical Mechanics (SCI)
Credits: 4.0 [max 4.0]
Typically offered: Fall Even Year
Kinematics and dynamics of a particle, oscillations, central-force motion, systems of particles, rigid-body rotations, gravitation, non-inertial coordinate systems, Lagrangian and Hamiltonian formulations, dynamics of rigid bodies. (4 hrs lect) prereq: 2101, Math 2101 or instr consent
PHYS 4101 - Electromagnetism
Credits: 4.0 [max 4.0]
Typically offered: Fall Odd Year
Vector calculus, electrostatics, Laplace and Poisson equations, dielectrics, magnetostatics, magnetic properties of matter, electromagnetic induction, Maxwell's equations, electrodynamics, electromagnetic waves. (4 hrs lect) prereq: 2101, Math 2101 or instr consent
PHYS 4201 - Quantum Mechanics
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Uncertainty principle, Schroedinger equation, commutation relations, momentum space wave functions, Dirac notation, applications to problems in one dimension and the hydrogen atom, angular momentum. (4 hrs lect) prereq: 2101, Math 2101
STAT 3601 - Data Analysis (M/SR)
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Nature and objectives of statistical data analysis, exploratory and confirmatory data analysis techniques. Some types of statistical procedures; formulation of models, examination of the adequacy of the models. Some special models; simple regression, correlation analysis, multiple regression analysis, analysis of variance, use of statistical computer packages. prereq: 1601 or 2601 or 2611 or instr consent
STAT 3611 - Multivariate Statistical Analysis (M/SR)
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Analysis of categorical data. Loglinear models for two- and higher-dimensional contingency tables. Logistic regression models. Aspects of multivariate analysis, random vectors, sample geometry and random sampling, multivariate normal distribution, inferences about the mean vector, MANOVA. Analysis of covariance structures: principal components, factor analysis. Classification and grouping techniques: discrimination and classification, clustering, use of statistical computer packages. prereq: 1601 or 2601 or 2611 or instr consent
STAT 4601 - Biostatistics
Credits: 4.0 [max 4.0]
Typically offered: Periodic Spring
Design and analysis of biological studies: biological assays, case-control studies, randomized clinical trials, factorial designs, repeated measures designs, observational studies, and infectious disease data. Analysis of survival data: basic concepts in survival analysis, group comparisons, and Cox regression model. Use of statistical computer packages. prereq: 1601 or 2601 or 2611 or instr consent