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Mathematics B.S.

Mathematics & Statistics
Swenson College of Science and Engineering
  • Program Type: Baccalaureate
  • Requirements for this program are current for Fall 2011
  • Required credits to graduate with this degree: 120
  • Required credits within the major: 51
  • Degree: Bachelor of Science
The program in mathematics develops competence in mathematical techniques and sharpens mathematical insight. Mathematics is fundamental to solving problems in physics, chemistry, biology, medicine, business, engineering, and technology. The mathematics major prepares students for careers in business, industry, and government and for further graduate studies. Note: the B.S. in statistics and actuarial science is listed separately. Honors Requirements: To graduate with department honors, a student must complete the program with an overall and department GPA of 3.50, satisfactorily complete a research project under the guidance of a department faculty member, and convey research results in a public presentation.
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
The Board of Regents, on recommendation of the faculty, grants degrees from the University of Minnesota. Requirements for an undergraduate degree from University of Minnesota Duluth include the following:
  1. Students must meet all course and credit requirements of the departments and colleges or schools in which they are enrolled including an advanced writing course. Students seeking two degrees must fulfill the requirements of both degrees. However, two degrees cannot be awarded for the same major.
  2. Students must complete all requirements of the Liberal Education Program.
  3. Students must complete a minimum of 120 semester credits.
  4. At least 30 semester credits must be earned through UMD, and 15 of the last 30 degree credits earned immediately before graduation must be awarded by UMD.
  5. Students must complete at least half of their courses at the 3xxx-level and higher at UMD. Study-abroad credits earned through courses taught by UM faculty and at institutions with which UMD has international exchange programs may be used to fulfill this requirement.
  6. If a minor is required, students must take at least three upper division credits in their minor field from UMD.
  7. For certificate programs, at least 3 upper-division credits that satisfy requirements for the certificate must be taken through UMD. If the program does not require upper division credits students must take at least one course from the certificate program from UMD.
  8. The minimum cumulative UM GPA required for graduation will be 2.00 and will include only University of Minnesota coursework. A minimum UM GPA of 2.00 is required in each UMD undergraduate major and minor. No academic unit may impose higher grade point standards to graduate.
  9. Diploma, transcripts, and certification will be withheld until all financial obligations to the University have been met.
Program Requirements
Requirements for the B.S. in mathematics include: * Minor or second major from another area of study.
Introduction to Calculus Courses (10 cr)
Calculus I
Take one of the following three Calculus I courses:
MATH 1290 - Calculus for the Natural Sciences [LE CAT2, LOGIC & QR] (5.0 cr)
or MATH 1296 - Calculus I [LE CAT, LOGIC & QR] (5.0 cr)
or MATH 1596 {Inactive} [LE CAT2, LOGIC & QR] (5.0 cr)
Take one of the following two Calculus II courses:
MATH 1297 - Calculus II [LOGIC & QR] (5.0 cr)
or MATH 1597 {Inactive} [LOGIC & QR] (5.0 cr)
Mathematics Core Courses (20 cr)
Core courses cannot count as electives. Take the following six courses:
MATH 3280 - Differential Equations with Linear Algebra (4.0 cr)
MATH 3355 - Discrete Mathematics (4.0 cr)
MATH 3941 - Undergraduate Colloquium (1.0 cr)
MATH 4201 - Elementary Real Analysis (4.0 cr)
MATH 4326 - Linear Algebra (3.0 cr)
STAT 3611 - Introduction to Probability and Statistics (4.0 cr)
Required From Other Departments (5 cr)
CS 1511 - Computer Science I [LE CAT3, LOGIC & QR] (5.0 cr)
WRIT 31xx
Electives (16 cr)
Core courses cannot count as electives. MATH elective courses must be at least 3100. STAT elective courses must be at least 5000. At least 10 credits of MATH and/or STAT electives must be 4xxx or above. At least 6 credits of electives must have MATH prefix and be 4xxx or above. Only one credit of MATH 3120 may count toward the math major. MATH 3326 or 4371 cannot be counted toward the major.
MATH
Take 0 - 6 credit(s) from the following:
· MATH 3xxx
MATH/STAT 4xxx-5xxx
Take 10 - 16 credit(s) from the following:
· MATH 4xxx
· MATH 5xxx
· STAT 5xxx
Double Majors ONLY
-A student pursuing a second major in statistics and actuarial science cannot apply STAT courses as electives. -A student with a second major other than statistics and actuarial science may substitute courses from the approved nondepartmental list (below) on a one elective MATH credit for two outside credits exchange basis for up to seven MATH elective credits. Approved Nondepartmental List:
Take 0 - 14 credit(s) from the following:
· BIOL 5807 - Mathematical Ecology (3.0 cr)
· CHE 4301 - Chemical Reaction Engineering (3.0 cr)
· CHE 4402 - Process Dynamics and Control (3.0 cr)
· CHEM 4641 - Physical Chemistry I (3.0 cr)
· CHEM 4642 - Physical Chemistry II (3.0 cr)
· CS 4511 {Inactive} (4.0 cr)
· CS 4521 {Inactive} (4.0 cr)
· CS 5222 - Artificial Intelligence (4.0 cr)
· CS 5212 - Computer Graphics (4.0 cr)
· CS 5232 - Introduction to Machine Learning and Data Mining (4.0 cr)
· EE 5151 - Digital Control System Design (3.0 cr)
· EE 5741 - Digital Signal Processing (3.0 cr)
· EE 5831 - Fuzzy Set Theory and Its Application (3.0 cr)
· GEOL 5240 - Physical Hydrogeology (4.0 cr)
· ME 4112 - Heat and Mass Transfer (3.0 cr)
· ME 4135 - Robotics and Controls (3.0 cr)
· PHYS 4001 - Classical Mechanics (4.0 cr)
· PHYS 4011 - Electromagnetic Theory (4.0 cr)
· PHYS 4021 - Quantum Physics II (4.0 cr)
· PHYS 4031 - Thermal and Statistical Physics (4.0 cr)
· PHYS 5052 - Computational Methods in Physics (3.0 cr)
· PHYS 5501 - Advanced Classical Mechanics (3.0 cr)
· PHYS 5541 - Fluid Dynamics (3.0 cr)
Program Areas of Emphasis
Mathematics includes a wide variety of areas in which students can specialize: traditional mathematics (preparation for Graduate School), applied analysis, computational mathematics, discrete mathematics, and mathematics education. Although no area is required for the MATH major, students are encouraged to work with their advisers to develop a coherent major plan. See the Department of Mathematics and Statistics Web page: http://www.d.umn.edu/math for descriptions of elective course groups.
 
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MATH 1290 - Calculus for the Natural Sciences (LE CAT2, LOGIC & QR)
Credits: 5.0 [max 5.0]
Course Equivalencies: 01420 - Math1290/1296/1596
Grading Basis: A-F or Aud
Typically offered: Every Fall & Spring
Differential and integral calculus needed for modeling in earth and life sciences. Computational software. Not intended for students in mathematics, engineering, or physical sciences. prereq: Math ACT 27 or higher or a grade of at least C- in Math 1250 or department consent
MATH 1296 - Calculus I (LE CAT, LOGIC & QR)
Credits: 5.0 [max 5.0]
Course Equivalencies: 01420
Grading Basis: A-F or Aud
Typically offered: Every Fall, Spring & Summer
First part of a standard introduction to calculus of functions of a single variable. Limits, continuity, derivatives, integrals, and their applications. prereq: Math ACT 27 or higher or a grade of at least C- in Math 1250 or department consent
MATH 1297 - Calculus II (LOGIC & QR)
Credits: 5.0 [max 5.0]
Course Equivalencies: 01421
Grading Basis: A-F or Aud
Typically offered: Every Fall, Spring & Summer
Second part of a standard introduction to calculus. Vectors, applications of integrals, transcendental functions, series, and multivariable functions and partial derivatives. prereq: A grade of at least C- in 1290 or 1296 or 1596
MATH 3280 - Differential Equations with Linear Algebra
Credits: 4.0 [max 4.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall, Spring & Summer
First, second, and higher order equations; series methods; Laplace transforms; systems; software; modeling applications; introduction to vectors; matrix algebra, eigenvalues. prereq: A grade of at least C- in 1297 or 1597
MATH 3355 - Discrete Mathematics
Credits: 4.0 [max 4.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall & Spring
Introduction to mathematical logic, predicates and quantifiers, sets, proof techniques, recursion and mathematical induction, recursive algorithms, analysis of algorithms, assertions and loop invariants, complexity measures of algorithms, combinatorial counting techniques, relations, graph theory. prereq: 1297 or 1597 or instructor consent, a grade of C- or better in is required in all prerequisite courses
MATH 3941 - Undergraduate Colloquium
Credits: 1.0 [max 1.0]
Grading Basis: S-N or Aud
Typically offered: Every Fall, Spring & Summer
Exposure to UMD mathematics-related colloquia. Sixteen points required: one for attending a colloquium; one for writing an acceptable report on a colloquium (at least four must be earned through writing); up to eight for giving a colloquium. prereq: Math major or minor, department consent; must register during semester of 16th point
MATH 4201 - Elementary Real Analysis
Credits: 4.0 [max 4.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall & Spring
In-depth study of concepts fundamental to the theory of single-variable calculus, including topology of the real numbers, convergence of sequences and series, function continuity, the derivative, and the Riemann integral. prereq: 3280, 3355, a grade of C- or better in is required in all prerequisite courses, no grad credit; credit will not be granted if already received for 3299
MATH 4326 - Linear Algebra
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall & Spring
Systems of linear equations, matrix algebra, determinants, vector spaces, subspaces, linear independence, span, basis, coordinates, linear transformations, matrix representations of linear transformations, eigenvalues and eigenvectors, diagonalization, Gram-Schmidt orthogonalization, orthogonal projection and least squares. prereq: A grade of at least C- in 3280, 3355, no grad credit
STAT 3611 - Introduction to Probability and Statistics
Credits: 4.0 [max 4.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall, Spring & Summer
Basic probability, including combinatorial methods, random variables, mathematical expectation. Binomial, normal, and other standard distributions. Moment-generating functions. Basic statistics, including descriptive statistics and sampling distributions. Estimation and statistical hypothesis testing. prereq: A grade of at least C- in Math 1290 or Math 1296
CS 1511 - Computer Science I (LE CAT3, LOGIC & QR)
Credits: 5.0 [max 5.0]
Course Equivalencies: 01383 - CS 1211/1511/1581
Grading Basis: A-F or Aud
Typically offered: Every Fall & Spring
A comprehensive introduction to computer programming using the C++ language. The course covers program design, C++ programming basics, control structures, functions and parameter passing. Students write and implement programs with data structures (arrays), pointers and files. Object-oriented programming is also introduced, along with concepts of abstraction, ADTs, encapsulation and data hiding. prereq: 3 1/2 yrs high school math or instructor consent
BIOL 5807 - Mathematical Ecology
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Fall Odd Year
Development and use of mathematical models to describe ecological patterns and processes. prereq: (2801, (Math 1290 or Math 1297)) or WRS or IBS Grad student
CHE 4301 - Chemical Reaction Engineering
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall & Summer
Theory of rates of chemical reactions. Application of rate data to design of batch, tubular, continuous stirred-tank, and catalytic-chemical reactors. prereq: BSChE candidate, 2121, 3112; no grad credit
CHE 4402 - Process Dynamics and Control
Credits: 3.0 [max 3.0]
Course Equivalencies: 01400
Grading Basis: A-F or Aud
Typically offered: Every Spring
Dynamic behavior of open-and closed-loop systems. Design and operation of automatic controllers for chemical process systems. The programming of a microcontroller. prereq: BSChE candidate, CHE 2121, 3031, 3112, (prereq or coreq 4301), Phys 2012 or 2015 and 2016; no grad credit
CHEM 4641 - Physical Chemistry I
Credits: 3.0 [max 3.0]
Prerequisites: 2 yrs chem,(2222 or 2212 or 2242), Math 3280, Phys 2012 or 2015 and 2016
Grading Basis: A-F or Aud
Typically offered: Every Fall
Quantitative treatment of physical principles and theories in chemistry, including topics in thermodynamics and kinetics. prereq: 2 yrs chem,(2222 or 2212 or 2242), Math 3280, Phys 2012 or 2015 and 2016
CHEM 4642 - Physical Chemistry II
Credits: 3.0 [max 3.0]
Prerequisites: 4641
Grading Basis: A-F or Aud
Typically offered: Every Spring
Quantitative treatment of physical principles and theories in chemistry, including topics in quantum mechanics and spectroscopy. prereq: 4641
CS 5222 - Artificial Intelligence
Credits: 4.0 [max 4.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall & Spring
Principles and programming methods of artificial intelligence. Knowledge representation methods, state space search strategies, and use of logic for problem solving. Applications chosen from among expert systems, planning, natural language understanding, uncertainty reasoning, machine learning, and robotics. Lectures and labs will utilize suitable high-level languages (e.g., Python or Lisp). prereq: grad student, 2511, (2531 or 3512 or MATH 3355) or instructor consent, a grade of C- or better is required in all prerequisite courses
CS 5212 - Computer Graphics
Credits: 4.0 [max 4.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall & Spring
Introduces the fundamentals of computer graphics to create 2D images from 3D data representations, the graphics pipeline, 3D representations of objects such as triangles and triangle meshes, surface material representations, color representation, vector and matrix mathematics, 3D coordinates and transformations, transport of light energy, global illumination, graphics rendering systemes, ray tracing, rasterization, real-time rendering, OpenGL and computer graphics hardware. prereq: graduate student, CS 2511, (2531 or 3512 or MATH 3355), (MATH 3280 or 3326) or instructor consent, a grade of C- or better is required in all prerequisite courses
CS 5232 - Introduction to Machine Learning and Data Mining
Credits: 4.0 [max 4.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall & Spring
Introduction to primary approaches to machine learning and data mining. Methods selected from decision trees, neural networks, statistical learning, genetic algorithms, support vector machines, ensemble methods, and reinforcement learning. Theoretical concepts associated with learning, such as inductive bias and Occam's razor. This is a potential Master's project course. prereq: grad student, 2511, 2531 or 3512 or MATH 3355, Stat 3611 or 3411, Math 3280 or 3326 or instructor consent; a grade of C- or better is required in all prerequisite courses
EE 5151 - Digital Control System Design
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Periodic Spring
Digital control system characteristics: transient and steady-state responses, frequency response, stability. Digital control system design using transform techniques. Controllability and observability. Design of digital control systems using state-space methods: pole placement and observer design, multivariable optimal control. Implementation issues in digital control prereq: 3151; credit will not be granted if already received for 4151
EE 5741 - Digital Signal Processing
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Periodic Spring
Discrete linear shift-invariant systems, z- & Fourier transform, sampling, discrete-time processing of signals, reconstruction of analog signals, filters and filter structures in direct, parallel, and cascaded forms, FIR & IIR digital filter design, impulse-invariant, bi-linear transform & window functions, FFT, introduction to image processing. prereq: 2111; credit will not be granted if already received for 4741
EE 5831 - Fuzzy Set Theory and Its Application
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Periodic Fall
Fuzzy sets and operations on fuzzy sets. Fuzzy relations and the extension principle. Linguistic variable and fuzzy IF-THEN rules. Fuzzy arithmetic. Fuzzy logic and approximate reasoning. Design of Fuzzy Systems from I/O data. Fuzzy logic--based control. Pattern Classifications. prereq: CS 1521, Math 3280; credit will not be granted if already received for 5831
GEOL 5240 - Physical Hydrogeology
Credits: 4.0 [max 4.0]
Grading Basis: A-F or Aud
Typically offered: Spring Even Year
Introduction to concepts of fluid movement in Earth's crust and the interaction of rocks and water. Introduction to the hydrologic cycle, theory of flow through porous media, crustal-scale flow systems, role of fluids in the plate tectonic cycle. prereq: 2110, Phys 2011 or 2013 and 2014, Math 1296 or Math 1290 or grad student or instructor consent; credit will not be granted if already received for 4240
ME 4112 - Heat and Mass Transfer
Credits: 3.0 [max 3.0]
Course Equivalencies: 01425 - ME 4112/ChE 3112
Grading Basis: A-F or Aud
Typically offered: Every Fall & Spring
Theory and practice of heat and mass transfer. Fundamentals of diffusion, conduction, convection, and radiation with application to the design of heat and mass transfer equipment and systems. prereq: 3111, Math 3298, BSME or BSChE candidate or instructor consent
ME 4135 - Robotics and Controls
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Periodic Fall
Exploration of Forward and Inverse Kinematics models for individual robots. Study of robot motion trajectories at the micro- and macroscopic level. Study of PE, PD and PID controllers for robots. Exploration of efficient methods for developing stable controllers for various geometric configurations. prereq: ME 3140, 3230, ENGR 2026 or ME 2226, BSME or BSIE or BSEP candidate or instructor consent
PHYS 4001 - Classical Mechanics
Credits: 4.0 [max 4.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall
Theoretical mechanics, including Lagrangian and Hamiltonian functions, symmetries, and conservation laws. prereq: 2022, Math 3280
PHYS 4011 - Electromagnetic Theory
Credits: 4.0 [max 4.0]
Grading Basis: A-F or Aud
Typically offered: Every Spring
Electric and magnetic fields, Maxwell's equations and applications, radiation. prereq: 3033
PHYS 4021 - Quantum Physics II
Credits: 4.0 [max 4.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall
Quantum wave mechanics with applications; Schrodinger equation, angular momentum, hydrogen atom, symmetries, identical particles. prereq: 3033
PHYS 4031 - Thermal and Statistical Physics
Credits: 4.0 [max 4.0]
Grading Basis: A-F or Aud
Typically offered: Every Spring
Elements of thermodynamics; principles of statistical physics applied to equilibrium properties of classical and quantum systems. prereq: 2021
PHYS 5052 - Computational Methods in Physics
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Fall Odd Year
Applications of numerical methods to problems in classical and quantum physics, emphasizing ordinary and partial differential equations. Computer modeling of physical systems and experimentation with simulations of physical systems. prereq: 2021, 1 sem programming, Math 3280
PHYS 5501 - Advanced Classical Mechanics
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Fall Odd Year
Hamiltonian and Lagrangian formulations for discrete systems, canonical transformations, nonlinear dynamics, and chaos theory. prereq: 4001
PHYS 5541 - Fluid Dynamics
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Spring Odd Year
Analytic and numeric treatment of dynamics of fluids. Rotating, stratified fluids, with applications in limnology, oceanography, and meteorology. prereq: 2022 or 2001, Math 3280