Duluth campus

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Duluth Campus

Mathematical Sciences Minor

Mathematics & Statistics
Swenson College of Science and Engineering
Link to a list of faculty for this program.
Contact Information
Department of Mathematics and Statistics, 140 Solon Campus Center, 1117 University Drive, Duluth, MN 55812 (218-726-8747; fax: 218-726-8399)
Email: mathstat@d.umn.edu
Website: https://scse.d.umn.edu/about/departments-and-programs/mathematics-statistics-department
  • Program Type: Graduate minor related to major
  • Requirements for this program are current for Spring 2023
  • Length of program in credits (master's): 6
  • Length of program in credits (doctoral): 12
  • This program does not require summer semesters for timely completion.
The Mathematical Sciences minor is for those wishing to pursue careers in other fields that use mathematics or statistics.
Program Delivery
  • via classroom (the majority of instruction is face-to-face)
Prerequisites for Admission
The preferred undergraduate GPA for admittance to the program is 3.00.
A strong background in mathematics and/or statistics.
Other requirements to be completed before admission:
Students interested in the minor are strongly encouraged to confer with their major field advisor and director of graduate studies, and the Mathematical Sciences director of graduate studies regarding feasibility and requirements.
For an online application or for more information about graduate education admissions, see the General Information section of this website.
Program Requirements
Use of 4xxx courses toward program requirements is permitted under certain conditions with adviser approval.
Minor coursework offered on both the A-F and S/N grading basis must be taken A-F, with a minimum grade of B- earned for each course.
Minor Coursework (6 to 12 credits)
Master’s students select 6 credits, and doctoral students select 12 credits from the following in consultation with the Mathematical Sciences director of graduate studies.
MATH 5201 - Real Variables (4.0 cr)
MATH 5327 - Advanced Linear Algebra (3.0 cr)
STAT 5571 - Probability (4.0 cr)
MATH 5233 - Mathematical Foundations of Bioinformatics (3.0 cr)
MATH 5202 - Applied Functional Analysis (3.0 cr)
MATH 5260 - Dynamical Systems (3.0 cr)
MATH 5270 - Modeling with Dynamical Systems (3.0 cr)
MATH 5280 - Partial Differential Equations (3.0 cr)
MATH 5810 - Linear Programming (3.0 cr)
MATH 8201 - Real Analysis (3.0 cr)
MATH 5330 - Theory of Numbers (3.0 cr)
MATH 5347 - Applied Algebra and Cryptology (3.0 cr)
MATH 5365 - Graph Theory (3.0 cr)
MATH 5366 - Enumerative Combinatorics (3.0 cr)
MATH 5372 - Abstract Algebra II (3.0 cr)
STAT 5411 - Analysis of Variance (3.0 cr)
STAT 5511 - Regression Analysis (3.0 cr)
STAT 5515 - Multivariate Statistics (3.0 cr)
STAT 5521 - Applied Time Series Analysis (3.0 cr)
STAT 5531 - Probability Models (4.0 cr)
STAT 5572 - Statistical Inference (4.0 cr)
STAT 8611 - Linear Models (3.0 cr)
Program Sub-plans
Students are required to complete one of the following sub-plans.
Students may not complete the program with more than one sub-plan.
Masters
Doctoral
  
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· Swenson College of Science and Engineering

View future requirement(s):
· Fall 2023

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MATH 5201 - Real Variables
Credits: 4.0 [max 4.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall
Limits, sequence and series of real numbers, tests for convergence, rearrangements, summability, and the class L-SQUARED. Metric spaces; continuous functions, connectedness, completeness, compactness. Banach fixed-point theorem and Piccard existence theorem for differential equations. prereq: 4201 with a grade of C- or better
MATH 5327 - Advanced Linear Algebra
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Spring
Vector spaces over fields, subspaces, linear transformations, matrix representations, change of basis, inner-product spaces, singular value decomposition, eigenspaces, diagonalizability, annihilating polynomials, Jordan form. prereq: Graduate student or instructor consent
STAT 5571 - Probability
Credits: 4.0 [max 4.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall & Spring
Axioms of probability. Discrete and continuous random variables and their probability distributions. Joint and conditional distributions. Mathematical expectation, moments, correlation, and conditional expectation. Normal and related distributions. Limit theorems. prereq: 3611, Math 3298, a grade of C- or better in is required in all prerequisite courses
MATH 5233 - Mathematical Foundations of Bioinformatics
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Spring
Mathematical, algorithmic, and computational foundations of common tools used in genomics and proteomics. Topics include: sequence alignment algorithms and implementations (Needleman-Wunsch, Smith-Waterman, BLAST, Clustal), scoring matrices (PAM, BLOSUM), statistics of DNA sequences (SNPs, CpG islands, isochores, satellites), and phylogenetic tree methods (UPGMA, parsimony, maximum likelihood). Other topics will be covered as time permits: RNA and protein structure prediction, microarray analysis, post-translational modification prediction, gene regulatory dynamics, and whole-genome sequencing techniques. prereq: MATH 3355, CS 1xxx or above, STAT 3411 or 3611
MATH 5202 - Applied Functional Analysis
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Spring Odd Year
Basic concepts, methods, and applications of functional analysis. Complete metric spaces, contraction mapping, and applications. Banach spaces and linear operators. Inner product and Hilbert spaces, orthonormal bases and expansions, approximation, and applications. Spectral theory of compact operators, including self-adjoint and normal operators. pre-req: MATH 5201, MATH 4326 or 5327; MATH 5327 can be taken concurrently
MATH 5260 - Dynamical Systems
Credits: 3.0 [max 3.0]
Typically offered: Fall Odd Year
Fundamentals of differential equations (existence, uniqueness, continuation of solutions); linear systems, autonomous systems, and Poincare-Bendixson theory; periodic systems; discrete dynamical systems; bifurcation theory; chaos. prereq: 3280 with a grade of C- or better
MATH 5270 - Modeling with Dynamical Systems
Credits: 3.0 [max 3.0]
Typically offered: Spring Even Year
Application and analysis of continuous and discrete dynamical systems. Model construction, simulation, and interpretation. prereq: 3280 with a grade of C- or better
MATH 5280 - Partial Differential Equations
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Fall Even Year
Introduction to partial differential equations, emphasizing use of Fourier series, Green's functions, and other classical techniques. prereq: A grade of at least C- in 3280 and 3298 or grad standing
MATH 5810 - Linear Programming
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Spring Odd Year
Motivation problems, modeling, theory of simplex method, duality and sensitivity analysis, large-scale problems, complexity, and Karmarkar algorithm. prereq: 3280 or 4326f with a grade of C- or better
MATH 8201 - Real Analysis
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Periodic Spring
Rigorous development of abstract measure spaces, measurable functions, and corresponding theory of integration. Lebesgue measure and Lebesgue integral developed as a particular model. (offered alt yrs) prereq: 5201 with a grade of C- or better
MATH 5330 - Theory of Numbers
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Spring Odd Year
Properties of integers, primes, divisibility, congruences, and quadratic reciprocity. Computational aspects include factoring algorithms and RSA cryptosystem. prereq: 3355 with a grade of C- or better or instructor consent
MATH 5347 - Applied Algebra and Cryptology
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Fall Even Year
Applied algebra topics include mathematical origami, permutation games, and the Rubik's cube. Cryptology topics include monoalphabetic substitution ciphers, RSA, primality testing, and elliptic curve cryptology, and recent advancements in the field. Only one of either MATH 4274 or MATH 5374 may be allowed for undergraduate mathematics electives. pre-req: grad student or instructor consent
MATH 5365 - Graph Theory
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall
Finite graphs, including trees, connectivity, traversability, planarity, colorability, labeling, and matchings. prereq: 3355 with a grade of C- or better or instructor consent
MATH 5366 - Enumerative Combinatorics
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Spring Odd Year
Permutations, combinations, binomial coefficients, inclusion-exclusion, recurrence relations, ordinary and exponential generating functions, Catalan numbers, selected topics from designs, finite geometries, Polya's enumeration formula. prereq: 3355 with a grade of C- or better
MATH 5372 - Abstract Algebra II
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Spring
Polynomial rings, divisibility in integral domains, field extensions, finite fields, special topic, and applications. prereq: 5371 with a grade of C- or better or instructor consent
STAT 5411 - Analysis of Variance
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Analysis of variance techniques as applied to scientific experiments and studies. Randomized block designs, factorial designs, nesting. Checking model assumptions. Using statistical computer software. prereq: 3411 or 3611; a grade of C- or better is required in all prerequisite courses
STAT 5511 - Regression Analysis
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall & Spring
Simple, polynomial, and multiple regression. Matrix formulation of estimation, testing, and prediction in linear regression model. Analysis of residuals, model selection, transformations, and use of computer software. prereq: 3611, Math 3280 or Math 4326, a grade of C- or better in is required in all prerequisite courses
STAT 5515 - Multivariate Statistics
Credits: 3.0 [max 3.0]
Typically offered: Fall Odd Year
Multivariate normal distribution, MANOVA, canonical correlation, discriminate analysis, principal components. Use of computer software. prereq: 5411 or 5511, Math 3280 or Math 4326, a grade of C- or better in is required in all prerequisite courses
STAT 5521 - Applied Time Series Analysis
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Spring
Characteristics of time series; time series regression and exploratory data analysis; introduction of ARIMA models, including model building, estimation and forecasting; spectral analysis and filtering. Use of statistical software R. prereq: Math 3280, Stat 3612 or 5511 or instructor consent
STAT 5531 - Probability Models
Credits: 4.0 [max 4.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall & Spring
Development of probability models and their applications to science and engineering. Classical models such as binomial, Poisson, and exponential distributions. Random variables, joint distributions, expectation, covariance, independence, conditional probability. Markov processes and their applications. Selected topics in stochastic processes. prereq: 3611, Math 1297 or Math 1597, a grade of C- or better in is required in all prerequisite courses, credit will not be granted if already received for STAT 4531.
STAT 5572 - Statistical Inference
Credits: 4.0 [max 4.0]
Grading Basis: A-F or Aud
Typically offered: Every Spring
Mathematical statistics; Bayes' and maximum-likelihood estimators, unbiased estimators; confidence intervals; hypothesis testing, including likelihood ratio tests, most powerful tests, and goodness-of-fit tests. prereq: STAT 3612 and 5571 with a grade of C- or better, credit will not be granted if already received for STAT 4572
STAT 8611 - Linear Models
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Fall Even Year
Developing statistical theory of general linear model. Distribution theory, testing, and estimation. Analysis of variance and regression. (offered alt yrs) prereq: 5572 with a grade of C- or better