We are searching data for your request:

**Forums and discussions:**

**Manuals and reference books:**

**Data from registers:**

**Wait the end of the search in all databases.**

Upon completion, a link will appear to access the found materials.

Upon completion, a link will appear to access the found materials.

## Courses

Course information found here includes all permanent offerings and is updated regularly whenever Academic Senate approves changes. For historical information, see the Course Catalogs. For actual course availability in any given term, use Course Search in the Portal.

#### [MATH 100] Introduction to Mathematical Thinking (1)

This course aims to give non-mathematics majors a sense of the importance of mathematics in human thought and an appreciation of the beauty and vitality of present-day mathematics. Material varies. Sample topics include combinatorial puzzles, number theory, tilings, networks, symmetries, map coloring, knots and surfaces, alternative number systems, and infinite sets. (1S) Offered occasionally. Prerequisite: Not open to students who have taken a mathematics course numbered 110 or higher or who have Advanced Placement credit for calculus.

#### [MATH 103] Cultural Approaches to Mathematics (1)

What we think of as “mathematical” ideas may be viewed by other cultures within the contexts of art, navigation, religion, record-keeping, games, or kin relationships. This course treats mathematical ideas investigated by cultures such as North and South American Indians, Africans, and various peoples of the Pacific Islands, and analyzes them through Western mathematics (developed in Europe, the Middle East, and India). The course helps the student understand what mathematics is, both to Western culture and to other cultures, and how cultural factors influenced the development of modern mathematics. (Also listed as Interdisciplinary Studies 103.) (2A) Offered once per year.

#### [MATH 104] Finite Mathematics (1)

An introduction to finite methods in mathematics: probability, graphs, linear programming, game theory, and patterns. The course emphasizes ways in which these methods can be used to build mathematical models applicable to the social and biological sciences. Offered occasionally. Prerequisite: 3 years of high school mathematics.

#### [MATH 106] Introduction to Statistical Concepts (1)

Introductory probability and statistics with illustrations from the behavioral, social, and natural sciences. Descriptive statistics, elementary probability, hypothesis testing, analysis of variance, contingency tables, linear regression and correlation, nonparametric tests. Offered each semester. Prerequisite: facility in high school algebra. Not open to students who have completed or are taking Mathematics 205, Anthropology 240, or Psychology 161.

#### [MATH 108] Pre-Calculus (1)

The mathematics necessary for calculus: algebraic manipulations radicals and exponents logarithmic, exponential and trigonometric functions graphing and analytical geometry theory of polynomials complex numbers, and how such mathematics is developed. This course is designed for students who wish to take calculus but are not adequately prepared by their high school background. Prerequisite: First- or second-year standing. Not open to juniors and seniors without departmental permission. Not open to students who have received credit for calculus.

#### [MATH 110] Calculus I (1)

An introduction to differential and integral calculus. Limits and continuity, derivatives and integrals of polynomial, trigonometric, exponential, and logarithmic functions, applications of derivatives to optimization and approximation, the Mean Value Theorem, and the Fundamental Theorem of Calculus. (1S) Offered each semester. Prerequisite: four years of high school mathematics, including trigonometry and either college algebra or precalculus.

#### [MATH 113] Calculus as Applied Mathematics (1)

Limits and continuity. Derivatives and integrals of the elementary functions and the basic theorems of calculus concepts, methods, and theorems illustrated by examples from biology, chemistry, geology, physics, and economics. Some use of Mathematica or Matlab in numerical and symbolic calculations. At least one project dealing with modeling. (1S) Offered once a year. Prerequisite: precalculus or four years of high school mathematics, including trigonometry and algebra. Open to students who have not taken Mathematics 110.

#### [MATH 115] Calculus II (1)

Techniques of integration, L’Hôpital’s Rule, infinite sequences and series, Taylor series and applications, first-order differential equations, and introduction to the calculus of multivariable functions, including partial derivatives and multiple integrals. (1S) Offered each semester. Prerequisite: Mathematics 110 or 113.

#### [MATH 117] Calculus Colloquium (.25)

Presentations by faculty, participants, and occasional guest speakers on a variety of topics related to calculus and its applications to other disciplines. Graded credit/no credit. Offered each fall. Prerequisite: concurrent enrollment in a mathematics course numbered 110 or higher or Advanced Placement credit for calculus.

#### [MATH 160] Discrete Structures (1)

Introduction to the mathematical basis for computer science, including logic, counting, graphs and trees, and discrete probability. Offered even years, fall semester. Prerequisite: Computer Science 111 and Mathematics 110 or 115.

#### [MATH 175] Linear Algebra (1)

Linear equations and matrices, abstract vector spaces and linear transformations, orthogonality, eigenvalues and eigenvectors. Emphasizes development of abstract thinking and a variety of applications of linear algebra in science and social science. (1S) Offered each semester. Prerequisite: Mathematics 115 some computer programming experience is desirable.

#### [MATH 190] Differential Equations (1)

Solution methods for first-order differential equations, linear differential equations, power-series solutions, the Laplace transform, numerical methods, stability, applications. Offered odd years, spring semester. Prerequisite: Mathematics 115.

#### [MATH 200] Combinatorics and Graph Theory (1)

Combinatorial counting principles, generating functions and recurrence relations, introduction to graph theory, graph-theoretic algorithms, and their implementation. Applications to operations research, computer science, and social science. Offered odd years. Prerequisite: Mathematics 115.

#### [MATH 201] Vector Calculus (1)

Differentiation and integration of functions of several variables integration on surfaces vector analysis theorems of Green, Stokes, and Gauss applications to ordinary and partial differential equations and to geometry. Offered even years, spring semester. Prerequisite: Mathematics 115.

#### [MATH 205] Mathematical Statistics I (1)

Probability calculus for discrete and continuous probability distributions of one and several variables, including order statistics, combining and transforming random variables, and the use of moment-generating functions. Introduction to hypothesis testing. Offered even years, fall semester. Prerequisite: Mathematics 115.

#### [MATH 208] Chaotic Dynamical Systems (1)

An introduction to the mathematical theory of dynamical systems, with special attention to systems exhibiting chaotic behavior. One-dimensional dynamics: fixed points, periodic orbits, chaotic orbits, and the transition to chaos. Two-dimensional dynamics: fractal images, Julia sets, and the Mandelbrot set. Includes computer experiments with chaotic systems applications. Offered odd years, spring semester. Prerequisite: Mathematics 115.

#### [MATH 215] Abstract Algebra (1)

Axiomatic treatment of selected algebraic structures including groups, rings, integral domains, and fields, with illustrative examples. Also includes elementary factorization theory. Offered each spring. Prerequisite: Mathematics 175.

#### [MATH 230] Topics in Geometry (1)

Topics chosen to illustrate modern approaches to geometry. May be repeated for credit if topic is different, with the approval of the department. Offered occasionally. Prerequisite: Mathematics 175, or other courses depending on the topic.

#### [MATH 240] Real Analysis (1)

The real numbers, metric concepts and continuity, differentiation and integration of real functions, infinite sequences and series of functions. Offered each fall. Prerequisite: Mathematics 175 or 208.

#### [MATH 270] Topics in Mathematics (.25 - 1)

Selected aspects of mathematics reflecting the interests and experience of the instructor. May be repeated for credit if topic is different. Offered occasionally. Prerequisite: varies with topic.

#### [MATH 300] Mathematical Modeling (1)

Construction and investigation of mathematical models of real-world phenomena, including team projects and use of computer packages as needed. Offered odd years, fall semester. Prerequisite: 1 unit of computer science and 2 mathematics courses numbered 175 or higher.

#### [MATH 310] Mathematical Statistics II (1)

Properties of point estimators, development of hypothesis tests by means of the generalized likelihood ratio, and inference using the normal and related distributions. One- and two-sample, goodness of fit, and distribution-free hypothesis tests. Inference for regression and analysis of variance. Offered odd years, spring semester. Prerequisite: Mathematics 205.

#### [MATH 335] Topology (1)

Topological invariants of knots, classification of compact surfaces, structure of three-dimensional manifolds. Introduction to homotopy groups and abstract topological spaces. Offered odd years, spring semester. Prerequisite: Mathematics 175 or 208.

#### [MATH 375] Complex Analysis (1)

The complex plane, analytic functions, complex integration, Taylor and Laurent series, residues and poles, conformal mapping, applications. Offered even years, spring semester. Prerequisite: Mathematics 175.

#### [MATH 380] Topics in Mathematics (.25 - 1)

Selected topics in mathematics, reflecting the interests and experience of the instructor. May be repeated for credit if topic is different. Offered occasionally. Prerequisite: varies with topic.

#### [MATH 385] Mathematics Colloquium (.5)

Attendance required. Students select a faculty guide to assist them in learning to research a mathematical topic, prepare preliminary drafts of a paper, finalize the paper using Latex typesetting software, and then present the results of the paper to the class in a 50-minute talk. Class includes talks by students, some faculty, and often guest speakers. The course may be taken more than once. (CP) Offered each semester. Prerequisite: Mathematics 175, junior standing.

#### [MATH 390] Special Projects (.25 - 1)

Individual guided investigations of topics or problems in mathematics. Since such investigation is important to the development of mathematical maturity, the department encourages each major to do at least one such project. Prerequisite: approval of the project by the department chair sophomore standing.

## Mathematics (MATH)

This is an archived copy of the 2018-19 catalog. To access the most recent version of the catalog, please visit http://bulletin.ndsu.edu.

**MATH 098. Intermediate Algebra. 3 Credits.**

Properties of the real number system, factoring, linear and quadratic equations, functions, polynomial and rational expressions, inequalities, systems of equations, exponents, and radicals. Offered through Continuing Education. Special fee required. Does not satisfy any requirements for graduation. A grade of C or higher is required in this course to be eligible to take MATH 103 or MATH 104.

**MATH 103. College Algebra. 3 Credits.**

Relations and functions, equations and inequalities, complex numbers polynomial, rational, exponential and logarithmic functions systems of equations, and matrices. Prereq: MATH 098 with a grade of C or higher or placement.

**MATH 104. Finite Mathematics. 3 Credits.**

Systems of linear equations and inequalities, matrices, linear programming, mathematics of finance, elementary probability and descriptive statistics. Prereq: MATH 098 with a grade of C or higher or placement.

**MATH 105. Trigonometry. 3 Credits.**

Angle measure, trigonometric and inverse trigonometric functions, trigonometric identities and equations, polar coordinates and applications. Prereq: MATH 103 or placement. Credit awarded only for MATH 105 or MATH 107, not both.

**MATH 107. Precalculus. 4 Credits.**

Equations and inequalities polynomial, rational, exponential, logarithmic and trigonometric functions inverse trigonometric functions algebraic and trigonometric methods commonly needed in calculus. An expedited, combined offering of MATH 103 and MATH 105. Prereq: Placement. Credit awarded only for MATH 105 or MATH 107, not both.

**MATH 128. Introduction to Linear Algebra. 1 Credit.**

Systems of linear equations, row operations, echelon form, matrix operations, inverses, and determinants. Prereq: MATH 105 or MATH 107. Credit awarded only for MATH 128 or MATH 129, not both.

**MATH 129. Basic Linear Algebra. 3 Credits.**

Systems of linear equations, matrices, determinants, vector spaces, lines and planes in space, linear transformations, eigenvalues and eigenvectors. Prereq: MATH 105 or MATH 107.

**MATH 144. Mathematics for Business. 4 Credits.**

Mathematics of finance, linear programming and its applications in business, limits, continuity, derivatives, implicit and logarithmic differentiation, higher order derivatives, optimization and extrema, partial differentiation, extreme values of functions of two variables. Prereq: MATH 103, MATH 107 or placement exam. Credit awarded only for MATH 144 or MATH 146, not both.

**MATH 146. Applied Calculus I. 4 Credits.**

Limits, derivatives, integrals, exponential and logarithmic functions and applications. Prereq: MATH 103, MATH 107, or placement. Credit awarded only for MATH 144 or MATH 146, not both.

**MATH 147. Applied Calculus II. 4 Credits.**

Definite integrals, trigonometry, introduction to differential equations, infinite sequences and series, probability and applications. Prereq: MATH 146.

**MATH 165. Calculus I. 4 Credits.**

Limits, continuity, differentiation, Mean Value Theorem, integration, Fundamental Theorem of Calculus and applications. Prereq: MATH 105, MATH 107, or placement.

**MATH 166. Calculus II. 4 Credits.**

Applications and techniques of integration polar equations parametric equation sequences and series, power series. Prereq: MATH 165.

**MATH 259. Multivariate Calculus. 3 Credits.**

Functions of several variables, vectors in two and three variables, partial derivatives, surfaces and gradients, tangent planes, differentials, chain rule, optimization, space curves, and multiple integrals. Prereq: MATH 166. Credit awarded only for MATH 259 or MATH 265, not both.

**MATH 265. Calculus III. 4 Credits.**

Multivariate and vector calculus including partial derivatives, multiple integration, applications, line and surface integrals, Green's Theorem, Stoke's Theorem, and Divergence Theorem. Prereq: MATH 166. Credit awarded only for MATH 259 or MATH 265, not both.

**MATH 266. Introduction to Differential Equations. 3 Credits.**

Solution of elementary differential equations by elementary techniques. Laplace transforms, systems of equations, matrix methods, numerical techniques, and applications. Prereq: MATH 259 or MATH 265. Coreq: MATH 128, MATH 129, or MATH 329.

**MATH 270. Introduction to Abstract Mathematics. 3 Credits.**

Sets, symbolic logic, propositions, quantifiers, methods of proof, relations and functions, equivalence relations, math induction and its equivalents, infinite sets, cardinal numbers, number systems. Prereq: MATH 166.

**MATH 329. Intermediate Linear Algebra. 3 Credits.**

Vector spaces over real and complex numbers, matrices, determinants, linear transformations, eigenvalues and eigenvectors, Cayley-Hamilton Theorem, inner product spaces, selected topics and applications. Prereq: MATH 129 and MATH 165.

**MATH 346. Metric Space Topology. 3 Credits.**

Various metrics on Euclidean spaces, metric spaces, open and closed sets, limit points and convergence, Bolzano Weierstrass Theorem, (uniformly) continuous functions, connected spaces, compact spaces and the Heine Borel Theorem, sequence of functions. Prereq: MATH 270.

**MATH 374. Special Problems In Mathematics. 1 Credit.**

Diverse and challenging mathematical problems are considered with the intent of preparing the student for the Putnam Mathematics competition. May be repeated for credit. Pass/Fail only. Prereq: MATH 270.

**MATH 376. Actuarial Exam Study. 1 Credit.**

Selected material from calculus, linear algebra, numerical analysis, and other areas that appear on national actuarial exams. May be repeated for credit. Pass/Fail only. Prereq: MATH 266 and MATH 429.

**MATH 420. Abstract Algebra I. 3 Credits.**

Groups, permutations, quotient groups, homomorphisms, rings, ideals, integers. Prereq: MATH 270 and MATH 329.

**MATH 421. Abstract Algebra II. 3 Credits.**

Division rings, integral domains, fields, field extensions, Galois Theory. Prereq: MATH 420.

**MATH 429. Linear Algebra. 3 Credits.**

Vector spaces, linear transformations, eigenvalues and eigenvectors, canonical forms, inner product spaces, and selected applications. Prereq: MATH 270.

**MATH 430. Graph Theory. 3 Credits.**

Graphs and directed graphs, graph models, subgraphs, isomorphisms, paths, connectivity, trees, networks, cycles, circuits, planarity, Euler's formula, matchings, bipartite graphs, colorings, and selected advanced topics. Prereq: MATH 270.

**MATH 436. Combinatorics. 3 Credits.**

Recurrence relations, formal power series, generating functions, exponential generating functions, enumeration, binomial coefficients and identities, hypergeometric functions, Ramsey theory, Sterling and Eulerian numbers. Prereq: MATH 270.

**MATH 439. Topics in Algebra and Discrete Mathematics. 3 Credits.**

Advanced topics in algebra and discrete mathematics. Topics may vary but may include: algebraic geometry, factorization, partially ordered sets, and/or coding theory. Prereq: MATH 420 or MATH 430 or MATH 436.

**MATH 440. Axiomatic Geometry. 3 Credits.**

Hilbert's axioms for Euclidean geometry, projective geometry, history of parallel axiom, hyperbolic geometry, elliptic geometry. Prereq: MATH 270.

**MATH 442. Introduction to Topology. 3 Credits.**

Basic Point-Set Topology: Topological Spaces, Open/Closed Sets, Continuity, Connectedness, Compactness Surfaces: Classification, Basic Invariants Introduction to Homology Applications: Brouwer's Fix-Point Theorem, Ham and Sandwich Theorem. Prereq: MATH 346.

**MATH 443. Differential Geometry. 3 Credits.**

Local and global geometry of plane curves, local geometry of hypersurfaces, global geometry of hypersurfaces, geometry of lengths and distances. Prereq: MATH 265 and MATH 346.

**MATH 449. Topics in Topology and Geometry. 3 Credits.**

Topics will vary and may include: Riemannian Geometry, Symplectic Topology, Dynamical Systems on Manifolds, Hamiltonian Systems, Geometric Group Theory, Descriptive Set Theory. Prereq: MATH 442 or MATH 443.

**MATH 450. Real Analysis I. 3 Credits.**

Differentiation and Riemann integration in the real numbers. Sequences and series of functions uniform convergence and power series. Prereq: MATH 346.

**MATH 452. Complex Analysis. 3 Credits.**

Complex number systems, analytic and harmonic functions, elementary conformal mapping, integral theorems, power series, Laurent series, residue theorem, and contour integral. Prereq: MATH 265 and MATH 270.

**MATH 453. Introduction to Lebesgue Measure. 3 Credits.**

Definition of Lebesgue measure. Measurable and Lebesgue integrable functions. Introduction to Lp spaces. Prereq: MATH 450.

**MATH 454. Introduction to Functional Analysis. 3 Credits.**

Functional analysis in sequence spaces. Standard sequence spaces and dual spaces. Hahn-Banach Theorem. Operators on sequences spaces. Prereq: MATH 346.

**MATH 459. Topics in Analysis. 3 Credits.**

Topics will vary and may include: Harmonic Analysis, Dynamical Systems, Fractals, Distribution Theory, and Approximation Theory. Prereq: MATH 450.

**MATH 460. Intensive Mathematica. 1 Credit.**

Thorough overview of the general purpose mathematical software MATHEMATICA: numerical and symbolic calculations for algebra and linear algebra, single and multivariable calculus, ordinary and partial differential equations, 2D- and 3D-graphics, animation, word processing. Prereq: MATH 259 or MATH 265.

**MATH 472. Number Theory. 3 Credits.**

Properties of integers, number theoretic functions, quadratic residues, continued fractions, prime numbers and their distribution, primitive roots. Prereq: MATH 270.

**MATH 473. Cryptology. 3 Credits.**

Cryptography and cryptanalysis of ciphers. Discrete logarithms, Diffie-Hellman key exchange, the RSA cryptosystem, elliptic curve cryptography, and selected topics. Prereq: MATH 420 or MATH 472.

**MATH 478. History of Mathematics. 3 Credits.**

Historical considerations emphasizing the source of mathematical ideas, growth of mathematical knowledge, and contributions of some outstanding mathematicians. Prereq: MATH 270.

**MATH 480. Applied Differential Equations. 3 Credits.**

Method of power series and method of Frobenius, oscillation theorems, special functions (Bessel functions and Legendre functions), linear systems including the exponential matrix. Sturm-Liouville and phase plane analysis as time permits. Prereq: MATH 266.

**MATH 481. Fourier Analysis. 3 Credits.**

Discrete and continuous Fourier transforms, Fourier series, convergence and inversion theorems, mean square approximation and completeness, Poisson summation, Fast-Fourier transform. Prereq: MATH 265.

**MATH 483. Partial Differential Equations. 3 Credits.**

First and second order partial differential equations, classification, examples, solution methods for the wave, diffusion, and Laplace equations, causality and energy, boundary value problems, separation of variables, Green's identities, Green's functions. Prereq: MATH 266 and either MATH 270 or Math 329.

**MATH 484. Mathematical Methodsof Biological Processes. 3 Credits.**

This course provides an introduction to mathematical methods in biology. Prereq: MATH 266.

**MATH 485. Topics in Applied Mathematics. 3 Credits.**

Topics will vary and may include: Models in Biology and Finance, Network Theory, Calculus of Variation, Stochastic Calculus, Integral Transforms, Control Theory, and Parameter Estimation. Prereq: MATH 483.

**MATH 488. Numerical Analysis I. 3 Credits.**

Numerical solution of nonlinear equations, interpolation, numerical integration and differentiation, numerical solution of initial value problems for ordinary differential equations. Prereq: MATH 266.

**MATH 620. Abstract Algebra I. 3 Credits.**

Groups, permutations, quotient groups, homomorphisms, rings, ideals, integers.

**MATH 621. Abstract Algebra II. 3 Credits.**

Division rings, integral domains, fields, field extensions, Galois Theory. Prereq: MATH 620.

**MATH 629. Linear Algebra. 3 Credits.**

Vector spaces, linear transformations, eigenvalues and eigenvectors, canonical forms, inner product spaces, and selected applications.

**MATH 636. Combinatorics. 3 Credits.**

Recurrence relations, formal power series, generating functions, exponential generating functions, enumeration, binomial coefficients and identities, hypergeometric functions, Ramsey theory, Sterling and Eulerian numbers.

**MATH 639. Topics in Algebra and Discrete Mathematics. 3 Credits.**

Advanced topics in algebra and discrete mathematics. Topics may vary but may include: algebraic geometry, factorization, partially ordered sets, and/or coding theory.

**MATH 640. Axiomatic Geometry. 3 Credits.**

Hilbert's axioms for Euclidean geometry, projective geometry, history of parallel axiom, hyperbolic geometry, elliptic geometry.

**MATH 642. Introduction to Topology. 3 Credits.**

Basic Point-Set Topology: Topological Spaces, Open/Closed Sets, Continuity, Connectedness, Compactness Surfaces: Classification, Basic Invariants Introduction to Homology Applications: Brouwer's Fix-Point Theorem, Ham and Sandwich Theorem.

**MATH 643. Differential Geometry. 3 Credits.**

Local and global geometry of plane curves, local geometry of hypersurfaces, global geometry of hypersurfaces, geometry of lengths and distances.

**MATH 649. Topics in Topology and Geometry. 3 Credits.**

Topics will vary and may include: Riemannian Geometry, Symplectic Topology, Dynamical Systems on Manifolds, Hamiltonian Systems, Geometric Group Theory, Descriptive Set Theory.

**MATH 650. Real Analysis I. 3 Credits.**

Differentiation and Riemann integration in the real numbers. Sequences and series of functions uniform convergence and power series.

**MATH 652. Complex Analysis. 3 Credits.**

Complex number systems, analytic and harmonic functions, elementary conformal mapping, integral theorems, power series, Laurent series, residue theorem, and contour integral.

**MATH 653. Introduction to Lebesgue Measure. 3 Credits.**

Definition of Lebesgue measure. Measurable and Lebesgue integrable functions. Introduction to Lp spaces.

**MATH 654. Introduction to Functional Analysis. 3 Credits.**

Functional analysis in sequence spaces. Standard sequence spaces and dual spaces. Hahn-Banach Theorem. Operators on sequences spaces.

**MATH 659. Topics in Analysis. 3 Credits.**

Topics will vary and may include: Harmonic Analysis, Dynamical Systems, Fractals, Distribution Theory, and Approximation Theory.

**MATH 660. Intensive Mathematica. 1 Credit.**

Thorough overview of the general purpose mathematical software MATHEMATICA: numerical and symbolic calculations for algebra and linear algebra, single and multivariable calculus, ordinary and partial differential equations, 2D- and 3D-graphics, animation, word processing.

**MATH 672. Number Theory. 3 Credits.**

Properties of integers, number theoretic functions, quadratic residues, continued fractions, prime numbers and their distribution, primitive roots.

**MATH 673. Cryptology. 3 Credits.**

Cryptography and cryptanalysis of ciphers. Discrete logarithms, Diffie-Hellman key exchange, the RSA cryptosystem, elliptic curve cryptography, and selected topics.

**MATH 678. History of Mathematics. 3 Credits.**

Historical considerations emphasizing the source of mathematical ideas, growth of mathematical knowledge, and contributions of some outstanding mathematicians.

**MATH 680. Applied Differential Equations. 3 Credits.**

Method of power series and method of Frobenius, oscillation theorems, special functions (Bessel functions and Legendre functions), linear systems including the exponential matrix. Sturm-Liouville and phase plane analysis as time permits.

**MATH 681. Fourier Analysis. 3 Credits.**

Discrete and continuous Fourier transforms, Fourier series, convergence and inversion theorems, mean square approximation and completeness, Poisson summation, Fast-Fourier transform.

**MATH 683. Partial Differential Equations. 3 Credits.**

First and second order partial differential equations, classification, examples, solution methods for the wave, diffusion, and Laplace equations, causality and energy, boundary value problems, separation of variables, Green's identities, Green's functions.

**MATH 684. Mathematical Methods of Biological Processes. 3 Credits.**

This course provides an introduction to mathematical methods in biology.

**MATH 685. Topics in Applied Mathematics. 3 Credits.**

Topics will vary and may include: Models in Biology and Finance, Network Theory, Calculus of Variation, Stochastic Calculus, Integral Transforms, Control Theory, and Parameter Estimation.

**MATH 688. Numerical Analysis I. 3 Credits.**

Numerical solution of nonlinear equations, interpolation, numerical integration and differentiation, numerical solution of initial value problems for ordinary differential equations.

**MATH 720. Algebra I. 3 Credits.**

Graduate level survey of algebra: rings, modules, linear algebra and selected advanced topics. Prereq or Co-req: MATH 621.

**MATH 721. Algebra II. 3 Credits.**

Graduate level survey of algebra: groups, fields, Galois theory, and selected advanced topics. Prereq: MATH 720.

**MATH 726. Homological Algebra. 3 Credits.**

An overview of the techniques of homological algebra. Topics covered will include categories and functors, exact sequences, (co)chain complexes, Mayer-Vietoris sequences, TOR and EXT. Applications to other fields will be stressed. Prereq: MATH 720.

**MATH 732. Introduction to Bioinformatics. 3 Credits.**

An introduction to the principles of bioinformatics including information relating to the determination of DNA sequencing. Prereq: STAT 661. Cross-listed with CSCI 732 and STAT 732.

**MATH 746. Topology I. 3 Credits.**

Topological spaces, convergence and continuity, separation axioms, compactness, connectedness, metrizability, fundamental group and homotopy theory. Advanced topics may include homology theory, differential topology, three-manifold theory and knot theory. Prereq: MATH 642.

**MATH 747. Topology II. 3 Credits.**

Topological spaces, convergence and continuity, separation axioms, compactness, connectedness, metrizability, fundamental group and homotopy theory. Advanced topics may include homology theory, differential topology, three-manifold theory and knot theory. Prereq: MATH 642.

**MATH 750. Analysis. 3 Credits.**

Lebesgue and general measure and integration theory, differentiation, product spaces, metric spaces, elements of classical Banach spaces, Hilbert spaces, and selected advanced topics. Prereq: MATH 650.

**MATH 752. Complex Analysis. 3 Credits.**

Analytic and harmonic functions, power series, conformal mapping, contour integration and the calculus of residues, analytic continuation, meromorphic and entire functions, and selected topics. Prereq: MATH 652.

**MATH 754. Functional Analysis. 3 Credits.**

Normed spaces, linear maps, Hahn-Banach Theorem and other fundamental theorems, conjugate spaces and weak topology, adjoint operators, Hilbert spaces, spectral theory, and selected topics. Prereq: MATH 750.

**MATH 756. Harmonic Analysis. 3 Credits.**

A survey of Harmonic analysis including: Lp spaces Fourier Series Fourier transform Hilbert transform and special selected topics. Prereq: MATH 750.

**MATH 760. Ordinary Differential Equations I. 3 Credits.**

Existence, uniqueness, and extensibility of solutions to initial value problems, linear systems, stability, oscillation, boundary value problems, and selected advanced topics. Prereq: MATH 650 or MATH 680.

**MATH 782. Mathematical Methods in Physics I. 3 Credits.**

Review of practical mathematical methods routinely used by physicists, including applications. Focus on differential equations, variational principles, and other selected topics. Cross-listed with PHYS 752.

**MATH 783. Mathematical Methods in Physics II. 3 Credits.**

Tensor analysis, matrices and group theory, special relativity, integral equations and transforms, and selected advanced topics. Prereq: MATH 629 and MATH 652. Cross-listed with PHYS 753.

**MATH 784. Partial Differential Equations I. 3 Credits.**

Classification in elliptic, parabolic, hyperbolic type existence and uniqueness for second order equations Green's functions, and integral representations characteristics, nonlinear phenomena. Prereq: MATH 650 or MATH 683.

**MATH 810. Research in the Teaching of University Mathematics. 3 Credits.**

This course will cover fundamental topics in mathematics education research including: research design, fundamental research areas, and the interconnection between research and classroom practices.

**MATH 824. Topics in Commutative Algebra. 3 Credits.**

Topics vary each time the course is offered and may include: dimension theory, integral dependence, factorization, regular rings, Cohen-Macaulay rings, Gorenstein rings. May be repeated for credit with change in subtopic. Prereq: MATH 720.

**MATH 825. Theory Of Rings. 3 Credits.**

The ideal theory of commutative rings, structure of (non-commutative) rings, and selected advanced topics. Prereq: MATH 720.

**MATH 830. Graph Theory. 3 Credits.**

Graduate-level survey of graph theory: paths, connectivity, trees, cycles, planarity, genus, Eulerian graphs, Hamiltonian graphs, factorizations, tournaments, embedding, isomorphism, subgraphs, colorings, Ramsey theory, girth. Prereq: MATH 630.

**MATH 836. Discrete Mathematics. 3 Credits.**

Combinatorial reasoning, generating functions, inversion formulae. Topics may include design theory, finite geometry, Ramsey theory, and coding theory. Advanced topics may include cryptography, combinatorial group theory, combinatorial number theory, algebraic combinatorics, (0,1)-matrices, and finite geometry. Prereq: MATH 636.

**MATH 849. Topics in Geometry & Topology. 3 Credits.**

Advanced topics in Geometry and/or Topology. Topics vary but may include: differential geometry, K-theory, knot theory, or noncommutative geometry. May be repeated for credit with change in subtopic. Prereq: MATH 642, MATH 643.

**MATH 856. Dynamical Systems. 3 Credits.**

A study of basic notions of topological and symbolic dynamics. Introduction to measurable dynamics and ergodic theory. Ergodicity, mixing and entropy of dynamical systems. Prereq: MATH 750.

**MATH 857. Topics in Functional Analysis. 3 Credits.**

Maximal monotone operators and the Hille-Yosida theorem, Sobolev spaces in dimension one and applications, Sobolev spaces in higher dimensions, extension operators, Sobolev embedding theorems, Poincare inequality, duality. May be repeated for credit with change in subtopic. Prereq: MATH 750. Co-req: MATH 751.

**MATH 861. Ordinary Differential Equations II. 3 Credits.**

Existence, uniqueness, and extendibility of solutions to initial value problems, linear systems, stability, oscillation, boundary value problems, difference equations, and selected advanced topics. Prereq: MATH 760.

**MATH 862. Integral Equations. 3 Credits.**

Existence and uniqueness of solutions of Fredholm and Volterra integral equations, Fredholm Theory, singular integral equations, and selected advanced topics. Prereq: MATH 650.

**MATH 864. Calculus Of Variations. 3 Credits.**

Variational techniques of optimization of functionals, conditions of Euler, Weierstrass, Legendre, Jacobi, Erdmann, Pontryagin Maximal Principle, applications, and selected advanced topics. Prereq: MATH 650.

**MATH 867. Topics in Applied Mathematics. 3 Credits.**

Topics will vary and may include: Optimal Control, Robust Control, Stability Analysis, Mathematics of Networks, Models in Biology, Levy Processes, Asymptotic Expansions. May be repeated for credit with change in subtopic. Prereq: MATH 650 or MATH 680.

**MATH 878. Modern Probability Theory. 3 Credits.**

Probability theory presented from the measure theoretic perspective. Emphasis on various types of convergence and limit theorems. Discussion of random walks, conditional expectations, and martingales. Prereq: STAT 768 or MATH 750. Cross-listed with STAT 778.

**MATH 880. Methods of Optimization. 3 Credits.**

Elements of convex analysis, constrained and unconstrained multi-dimensional linear and nonlinear optimization theory and algorithms, convergence properties and computational complexity. Prereq: CSCI 653. Cross-listed with CSCI 880.

**MATH 881. Mathematical Control Theory. 3 Credits.**

Standard optimal control and optimal estimation problems duality optimization in Hardy space robust control design. Prereq: MATH 650.

**MATH 885. Partial Differential Equations II. 3 Credits.**

Nonlinear partial differential equations, Non-variational techniques, Hamilton-Jacobi equations, Riemann invariants, Entropy/entropy-flux pairs, selected advanced topics. Prereq: MATH 784.

**MATH 888. Numerical Analysis. 3 Credits.**

Numerical solutions to partial differential and integral equations, error analysis, stability, acceleration of convergence, numerical approximation, and selected advanced topics. Prereq: MATH 688.

Copyright © North Dakota State University all rights reserved. Published by the Office of Registration and Records

## Mathematics (MAT)

This course is intended for students in non-quantitative majors whose core math class is Math 102 or Math 134. The course covers applications from arithmetic, including LCD, GCF, fractions, decimals, percent, ratio and proportion, and unit conversions. Topics from algebra include solving linear equations and using formulas. Real world applications, a focus on problem solving and the use of inductive and deductive reasoning are emphasized throughout.

This course is designed to strengthen basic mathematical skills within problem-solving contexts. This course includes the real number system, basic arithmetic and algebraic operations, algebra, equations, inequalities, financial mathematics and geometry.

This course is designed to strengthen basic mathematical skills within problem-solving contexts. This course includes the real number system, basic arithmetic and algebraic operations, algebra, equations, inequalities, financial mathematics and geometry.

This course is designed to strengthen basic mathematical skills within problem-solving contexts. This course includes the real number system, basic arithmetic and algebraic operations, algebra, equations, inequalities, financial mathematics and geometry.

Students will develop proficiency in arithmetic, including fractions, decimals and percent, and algebra, including solving linear equations and inequalities, the arithmetic of polynomials and rational expressions, and graphing lines. Particular focus will be on applied problems and translating word problems into algebra and solving. There is no credit or grades assigned in this course, but successful completion will give the student the opportunity to retake the Mathematics Placement Exam.

Investigation and applications of appropriate mathematical subject matter drawn from algebra, combinatorics and probability, logic, statistics, financial mathematics and geometry.

Investigation and applications of appropriate mathematical subject matter drawn from algebra, combinatorics and probability, logic, statistics, financial mathematics and geometry.

Investigation and applications of appropriate mathematical subject matter drawn from algebra, combinatorics and probability, logic, statistics, financial mathematics and geometry.

This paired learning community is geared for those whose majors do not require a specific math class and who would like to explore cultural issues in depth. These courses will examine stereotypes of gender, race, and class from ancient to modern times through the lens of mathematical studies. We will examine how these three categories intersect and become intertwined in social reality. How can math be used to describe and analyze those realities?

Topics in algebra selected from properties of real numbers, simplification of algebraic expressions, factoring, exponents and radicals, equations, inequalities, logarithms, functions and their graphs, systems of linear equations, applications to business and the mathematics of finance. Note: Students may have this course waived as a prerequisite if their background warrants it. This waiver is usually determined by the Mathematics Placement Exam.

Does not satisfy the core in Mathematics. The algebra content of this course is the same as MAT 103, Algebra, with the addition of foundational mathematics in the earlier part of the course. These additional topics include integers, fractions, decimals, percents, and proportions.

Does not satisfy the core in Mathematics. The algebra content of this course is the same as MAT 103, Algebra, with the addition of foundational mathematics in the earlier part of the course. These additional topics include integers, fractions, decimals, percents, and proportions.

Topics in algebra selected from properties of real numbers, simplification of algebraic expressions, factoring, exponents and radicals, equations, inequalities, logarithms, functions and their graphs, systems of linear equations, applications to business and the mathematics of finance. Note: Students may have this course waived as a prerequisite if their background warrants it. This waiver is usually determined by the Mathematics Placement.

Does not satisfy the core in Mathematics. The algebra content of this course is the same as MAT 103, Algebra, with the addition of foundational mathematics in the earlier part of the course. These additional topics include integers, fractions, decimals, percents, and proportions.

This course is identical in content to Math 103 but will be offered as a no credit/no fee course for incoming students in the Early Start Math Program. Course will not appear on students’ transcripts. Successful completion will allow students to retake the Mathematics Placement Exam.

A brief review of algebra and its applications to business. Solutions systems of linear equations introduction to matrix algebra and its applications. Foundations of finite probability, interpretations of probability, equally-likely outcomes, independent events, conditional probability, Bayes’ theorem frequency distributions, random variables, probability mass functions and cumulative distributions, binomial and normal distribution and their applications. Mathematics of finance and its applications.

Introduction to linear programming, the corner point and simplex methods for solving linear programs, foundations of finite probability, interpretations of probability, equally-likely outcomes, independent events, conditional probability, Bayes' theorem, and mathematics of finance.

This course covers in greater depth the material described under MAT 103. Additional topics to be selected from linear programming, introduction to matrix algebra, Markov chains, game theory.

The course focuses on the structure of modern mathematics as it is used today. It emphasizes critical thinking, arithmetic algorithms, number systems, and problem solving. Topics include: strategies of problem solving, Boolean logic, sets, relations, functions, study of the integers, rational numbers, real numbers, and introduction to mathematical computer packages.

This course is a continuation of themes of MAT 109A. Topics include the rudiments of probability, introduction to basic statistics, plane geometry, coordinate geometry, transformation geometry, measurement of plane figures, and the metric system.

Limits, continuity, derivatives of algebraic, exponential and logarithmic functions, optimization problems, introduction to integral calculus, fundamental theorem of integral calculus. Business and economic applications are stressed throughout.

This course combines the beauty and fascination of astronomy with the logical reasoning and problem solving techniques of mathematics. Students will learn connections between science and mathematics and study real-world problem solving processes, as well as customary topics in both subjects. Students will interactively learn to use an astronomical telescope to take measurements and obtain a practical understanding of astronomy. Typical problems in astonomy will be presented to students who will then in turn learn to solve them in the mathematics portion of the course. Field trips: Hayden Planetarium. Field work: 6-8 sessions outside with telescopes.

Collection, tabulation, and graphing of statistical data measures of location and dispersion sampling and sampling distributions confidence intervals hypothesis testing correlation and regression. Business and economic applications are stressed throughout.

This course in technical mathematics covers topics in algebra and geometry. Topics include: functions and their graphs, trigonometry, base conversion, logarithms, and binary sequences. A brief review of numbers and basic algebra will lead to a further and more detailed exploration of the aforementioned topics.

Precalculus course for students who require additional mathematical background prior to taking MAT 131. Topics include logarithmic and exponential functions, trigonometric functions, trigonometric identities, solving triangles, conic sections, solving equations.

Preliminary precalculus course for students who require additional mathematical background prior to taking MAT 131. Topics include logarithmic and exponential functions, trigonometric functions, trigonometric identities, solving triangles, conic sections, solving equations.

Analytic geometry, continuity, derivatives and differentials, applications to graphing and optimization problems, introduction to anti-differentiation and the definite integral.

Applications of the definite integral, techniques of integration, indeterminate forms, improper integrals, Taylor's formula, infinite series.

Introduction to the study of random processes finite sample spaces, the role of assumptions in the formulation of probability models, probability models based on equally-likely outcomes, independent events, and conditional probability. Bayes' theorem, random variables, mathematical expectation statistical applications of probability, introduction to sampling theory, confidence intervals and hypothesis testing.

An introductory course in discrete mathematical structures. Selected topics chosen from set theory, number systems, logic and proofs, combinatorics and graphs, computer applications to real world problems.

This course provides a non-calculus based introduction to statistics, with a focus on applications in the life sciences: biology, chemistry and health care. Topics covered include data gathering, numerical and graphical data summaries, elementary probability, binomial, normal and sampling distributions, confidence intervals hypothesis testing, regression and correlation, analysis of variance, and nonparametric statistics. This course includes the use of technology.

This is an elementary introduction to statistics focusing on principles and techniques pertinent to psychology. Topics include graphical and numerical data presentation and summarization, elementary probability and relevant sampling distributions, correlation, point and confidence interval estimation, hypothesis testing, and chi-square test for goodness of fit. The software statistical package SPSS is taught and employed throughout the course.

This course focuses on those statistical methods that are relevant to the Social Sciences. A variety of applications related to this area are discussed. Statistical packages are introduced and utilized. Topics are chosen from both descriptive and inferential statistics.

This course is an introduction to probability and statistics designed to illustrate applications to economics and business economics. Topics include: descriptive statistics, data collection, basic probability, Bayes’ Theorem, sampling and sampling distributions confidence intervals hypothesis testing correction and regression. Statistical software will be used as an integral part of this course.

## Majors

### How to Read Course Descriptions

The **bold** first line is the capitalized course abbreviation that designates the subject area followed by the course number, title and credits.

**Prerequisite:** Coursework to be completed and/or requirements to be met before taking the course.

**Course description:** Summary of the purpose and key topical areas of the course.

**Attributes:** Indicates Liberal Education (LE) (or General Education-GE) area for which the course may fulfill a requirement and/or special course fee requirements.

NOTE: Attributes are term specific to the term course is taken. Defer to the Schedule of Classes in CampS for term specific attributes.

GE – General Education applies to requirements in catalogs prior to Fall 2016.

Courses listed in the prerequisite that are not linked indicate that the course is inactive and is listed for historical purposes.

The unit of credit is the semester hour. It is defined as one class hour per week (or its equivalent) for one semester. Thus, a lecture-discussion course which meets three hours per week ordinarily carries three semester credits. Laboratory and studio classes usually require two hours in class as the equivalent of one semester credit.

**DS 700 Foundations of Data Science (3 crs)**

Prerequisite: Limited to Data Science master's degree students.

Introduction to data science and its importance in business decision making.

Attributes: Data Science MS OL Flat Rate Tuition, Special Course Fee Required

Grading Basis: A-F Grades Only

Lecture/Discussion Hours: 3

**DS 705 Statistical Methods (3 crs)**

Prerequisite: Limited to Data Science master's degree students.

Statistical methods and inference procedures presented with an emphasis on applications, computer implementation, and interpretation of results.

Attributes: Data Science MS OL Flat Rate Tuition, Special Course Fee Required

Grading Basis: A-F Grades Only

Lecture/Discussion Hours: 3

**DS 710 Programming for Data Science (3 crs)**

Prerequisite: Limited to Data Science master's degree students.

Introduction to programming languages and packages used in data science.

Attributes: Data Science MS OL Flat Rate Tuition, Special Course Fee Required

Grading Basis: A-F Grades Only

Lecture/Discussion Hours: 3

**DS 715 Data Warehousing (3 crs)**

Prerequisite: Limited to Data Science master's degree students.

Introduction to the concepts and techniques to work with and reason about subject-oriented, integrated, time-variant, and nonvolatile collections of data in support of management’s decision-making process.

Attributes: Data Science MS OL Flat Rate Tuition, Special Course Fee Required

Grading Basis: A-F Grades Only

Lecture/Discussion Hours: 3

**DS 730 Big Data: High Performance Computing (3 crs)**

Prerequisite: Limited to Data Science master's degree students.

Overview of how to process large datasets efficiently, including introduction of non-relational databases.

Attributes: Data Science MS OL Flat Rate Tuition, Special Course Fee Required

Grading Basis: A-F Grades Only

Lecture/Discussion Hours: 3

**DS 735 Communicating about Data (3 crs)**

Prerequisite: Limited to Data Science master's degree students.

Prepares students to master technical, informational, and persuasive communication to meet organizational goals.

Attributes: Data Science MS OL Flat Rate Tuition, Special Course Fee Required

Grading Basis: A-F Grades Only

Lecture/Discussion Hours: 3

**DS 740 Data Mining & Machine Learning (3 crs)**

Prerequisite: Limited to Data Science master's degree students.

Data mining methods and procedures for diagnostic and predictive analytics.

Attributes: Data Science MS OL Flat Rate Tuition, Special Course Fee Required

Grading Basis: A-F Grades Only

Lecture/Discussion Hours: 3

**DS 745 Visualization and Unstructured Data Analysis (3 crs)**

Prerequisite: Limited to Data Science master's degree students.

Covers various aspects of data analytics including visualization and analysis of unstructured data such as social networks.

Attributes: Data Science MS OL Flat Rate Tuition, Special Course Fee Required

Grading Basis: A-F Grades Only

Lecture/Discussion Hours: 3

**DS 760 Ethics of Data Science (3 crs)**

Prerequisite: Limited to Data Science master's degree students.

Ethical issues related to data science, including privacy, intellectual property, security, and the moral integrity of inferences based on data.

Attributes: Data Science MS OL Flat Rate Tuition, Special Course Fee Required

Grading Basis: A-F Grades Only

Lecture/Discussion Hours: 3

**DS 775 Prescriptive Analytics (3 crs)**

Prerequisite: Limited to Data Science master's degree students.

Procedures and techniques for using data to inform decision making. Topics include optimization, decision analysis, game theory, and simulation.

Attributes: Special Course Fee Required

Grading Basis: A-F Grades Only

Lecture/Discussion Hours: 3

**DS 780 Data Science and Strategic Decision Making (3 crs)**

Prerequisite: Limited to Data Science master's degree students.

The interaction between data science and strategic decision making. Leveraging data resources for competitive advantage in the marketplace.

Attributes: Data Science MS OL Flat Rate Tuition, Special Course Fee Required

Grading Basis: A-F Grades Only

Lecture/Discussion Hours: 3

**DS 785 Data Science Capstone (3 crs)**

Prerequisite: Limited to Data Science master's degree students.

Capstone course students will develop and execute a data science project using real-world data and communicate results to a non-technical audience.

Attributes: Data Science MS OL Flat Rate Tuition, Special Course Fee Required

Grading Basis: A-F Grades Only

Lecture/Discussion Hours: 3

## Mathematics (MATH)

Credits: 4

Prerequisite: Qualifying placement score or completion of ASC 93 with a grade of a C or better.

Typically Offered: FASPSU

Solutions of linear and quadratic equations and inequalities, graphing functions and relations, polynomial and rational functions, systems of equations and inequalities, exponential and logarithmic functions.

**MATH 104. Finite Mathematics**

Credits: 3

Prerequisite: Qualifying placement score or completion of ASC 93 with a grade of C or better.

Typically Offered: FALLSPR

Topics include functions, matrices, modeling, linear systems, linear programming, the simplex method, probability and statistics, and mathematics of finance.

**MATH 105. Trigonometry**

Credits: 2

Prerequisite: Math 103.

Typically Offered: FALLSPR

Functions of the general angle, graphs of the trigonometric functions, inverse functions, identities, trigonometric equations, and applications.

**MATH 107. Pre-Calculus**

Credits: 4

Prerequisite: Qualifying placement score or completion of ASC 93 with a grade of C or better.

Typically Offered: FALLSPR

Selected topics from algebra and trigonometry with special emphasis on how they apply to the study of calculus. Topics covered include solutions of equations and inequalities, exponential, logarithmic, trigonometric and circular functions and their graphs.

**MATH 137. Applied Algebra**

Credits: 3

Prerequisite: Qualifying placement score or completion of ASC 91 with a grade of C or better.

Typically Offered: FASPSU

An intermediate algebra course for students enrolled in technology programs. Topics include properties of real numbers, algebraic expressions, factoring, formula manipulation, graphing, linear equations, quadratic equations, solving systems of equations, simultaneous equations, exponents, radicals and logarithmic equations. NOTE: This course satisfies general education requirements for the AAS, diploma and certificate, but not for the AA and AS degrees. Refer to the online catalog for updated placement information.

**MATH 146. Applied Calculus I**

Credits: 3

Prerequisite: MATH 103 or MATH 104.

Typically Offered: FALLSPR

Limits, continuity, differentiation, integration and differential equations are included with many examples drawn from business, economics, management, life and social sciences.

**MATH 165. Calculus I**

Credits: 4

Prerequisite: Math 107 or MATH 103 and MATH 105 or qualifying placement score.

Typically Offered: FASPSU

Review of analytic geometry, limits and continuity, derivatives of functions of one variable with applications, L'Hopital's rule, antidifferentiation, the Fundamental Theorem of Calculus, numerical integration, trigonometric, exponential and logarithmic functions.

**MATH 166. Calculus II**

Credits: 4

Prerequisite: MATH 165.

Typically Offered: FASPSU

Applications of the definite integral, areas, volumes of solids of revolution, surface areas, centroids, techniques of integration, parametric equations, polar equations, improper integrals, and tests of convergence for sequences and series.

**MATH 208. Discrete Mathematics**

Credits: 3

Prerequisite: MATH 103 or qualifying placement score.

Typically Offered: SPRING

Study of sets, relations, functions, graph theory, Boolean algebra, combinatorics, logic and induction with particular emphasis on their application to computer science.

**MATH 210. Elementary Statistics**

Credits: 3

Prerequisite: Qualifying placement score or completion of ASC 93 with a grade of C or better.

Typically Offered: FASPSU

An introduction to statistical methods of gathering, presenting and analyzing data. Topics include probability and probability distributions, confidence intervals, hypothesis testing, and linear regression and correlation.

**MATH 220. Probability and Statistics**

Credits: 3

Prerequisite: MATH 166 or concurrent enrollment in MATH 166.

Typically Offered: SPRING

Study of basic probability theory including probability functions for both discrete and continuous data. Sampling distributions, point and interval estimations, hypothesis testing and regression and correlation theory are also explored with emphasis placed on applications of each method.

**MATH 227. Applied Linear Algebra**

Credits: 3

Prerequisite: MATH 166 or concurrent enrollment in MATH 166.

Typically Offered: FALL

Vectors and matrices, systems of linear equations and inequalities, mappings, determinants, linear programming and the simplex method.

**MATH 265. Calculus III**

Credits: 4

Prerequisite: MATH 166.

Typically Offered: FALLSPR

Vectors and the geometry of space, functions of several variables with applications, lines and planes in space, gradient vectors and directional derivatives, multiple integration with applications, divergence and curl, line and surface integrals.

**MATH 266. Introduction to Differential Equations**

Credits: 3

Prerequisite: MATH 265.

Typically Offered: SPRING

Study of first and second order differential equations, linear differential equations, Laplace transforms, systems of equations, approximate solutions by numerical methods, eigenvalues and eigenvectors. Special emphasis is given to applications in a variety of fields.

**MATH 277. Mathematics for Elementary Teachers I**

Credits: 4

Prerequisite: MATH 103.

Typically Offered: FALL

Sets, divisibility, primes, number systems, number bases other than ten, number theory and problem solving. This class is designed specifically for elementary education majors.

**MATH 278. Math for Elementary Teachers II**

Credits: 3

Prerequisite: MATH 277.

Typically Offered: SPRING

A mathematics content course for prospective elementary school teachers that integrates the understanding of content and development of processes. Topics include real numbers, proportional reasoning, elementary algebra, geometry and probability. Appropriate use of calculators, computers and manipulatives are used in the course.

Bismarck State College

PO Box 5587

1500 Edwards Ave

Bismarck, ND 58506

701-224-5400 or 1-800-445-5073

## Computer Science Program Description

Courses in computer science are designed to educate students of the liberal arts in computer literacy to provide computer programming instruction for students of mathematics, science, business and social science and to establish a solid foundation in computer software theory and practice for students of all disciplines. The courses are taught by the Mathematics Department. The College offers a major in Computing and Applied Mathematics that combines mathematics and computer science (see Mathematics), a concentration in Management Information Systems within the Business Administration major (see Business Administration and Economics), and a minor outlined below.

Saint Mary’s has a long history of providing quality international programs as an essential part of our educational mission—forming women leaders who will make a difference in the world. As this world becomes increasingly interdependent, the College offers an expanding range of semester, year, semester break, and summer study and service programs in a wide variety of countries, and encourages students to take advantage of them. Learn more about the various Study Abroad opportunities.

For math majors, there is a unique opportunity to study abroad in the Budapest Semesters in Mathematics program. Students wishing to study abroad through this program may do so any semester or over the summer after they have completed either MATH 341 Analysis I or MATH 353 Abstract Algebra I (though exceptions have been made).

## Elective Course Offerings Fall 2021

### Dance

In addition to the dance courses listed under Creative and Performing Arts, the following courses are available for elective credit. For both Sophia and elective dance courses, students receive two credit hours for technique courses taken for the first time and one credit hour for subsequent enrollment in the same level technique course. All two-credit technique courses include an academic component: required and recommended literary sources, as well as written midterm and final examinations that test knowledge of terminology and movement concepts.

The ensemble functions as the student dance company in residence. The dancers meet on a regular basis for technique classes, master classes and rehearsals with faculty and guest choreographers. D.E.W. presents an annual concert. Variable credit offered for performance and production. Performance students must be concurrently enrolled in a technique class. May be repeated for a maximum of 9 credits. By audition/permission only.

### Environmental Studies

**ENVS 203 Sustainability at Saint Mary’s College and in the Holy Cross Charism (2)**

This course will address sustainability in the context of the local academic community and its institutions. In light of the recent papal encyclical, Laudato si, On Care for Our Common Home, this course will provide students an opportunity to explore in an interdisciplinary way the challenges of sustainability and develop collaborative strategies for making our common campus homes more sustainable. This course will be offered concurrently at ND, SMC, and HCC, and will be co-taught by faculty from all three campuses. It will meet in rotation on each of the three campuses once per week for two hours. Students will be invited to examine the course materials in conversation with the mission of the Congregation of Holy Cross through immersion at each of the campuses and encounters with the sisters, brothers, and priests of Holy Cross and with sustainability professionals. *This course satisfies LO3 Social Responsibility but does not fulfill an LO1 requirement.*

### Music

Beginning piano for those with no previous keyboard experience, using the electronic piano lab. Designed to develop music skills through correlation of music fundamentals with beginning piano literature, including folk songs, holiday songs, easy classics, and blues.

**MUS 201 Collegiate Choir (1)**

A women’s choir that performs primarily on campus. Goals include developing excellent individual and group tone quality, working toward clear and proper diction, and strengthening aural and music reading abilities. Performs quality women’s repertoire, both sacred and secular, in 2–4 parts. Membership by audition only. Auditions will take place during August orientation through the first week of classes.

**MUS 203 Women's Choir (1)**

This is the College’s select women’s ensemble which performs music of all periods with an emphasis on new music. The choir regularly commissions and records new works, takes national concert tours every other year, and makes Carnegie Hall appearances every four years. The ensemble has regular performances with the South Bend Symphony Orchestra and hosts the annual High School Women’s Choir Festival. Membership is by audition only which will take place during August orientation through the first week of classes.

String Ensemble is a non-auditioned string (winds and percussion will be allowed when appropriate) ensemble open to all members of the college community. The course includes the study and performance of significant string literature. May be repeated for credit.

Concert band is a non-auditioned instrumental ensemble open to all members of the college community. The course includes the study and performance of significant concert band literature. May be repeated for credit.

A bell ensemble that provides music for campus liturgies and music department activities.

### Philosophy

**PHIL 291 Dialogue and Civil Discourse (1)**

Building a strong community means engaging with people whose backgrounds, beliefs and experiences are different from yours. In this course, students will develop skills to engage in constructive dialogue with others who have different views on social and political issues. The class will discuss a controversial contemporary issue each week (for example: abortion, free speech on campus, immigration, the 2 nd Amendment and gun control). Readings will consist of contemporary media articles drawn from a range of sources and viewpoints. Students will investigate their own core assumptions and beliefs about key issues and will listen to the views and experiences of others in the class.

*This course satisfies LO3 Social Responsibility and LO3 Intercultural Competence but does not fulfill an LO1 requirement. One section offered for first-year students only.*### Physical Education

The Physical Education Department offers selected activity courses based on student needs and interests. These courses are offered throughout the day and week to satisfy a broad range of fitness interests. You can de-stress with yoga or work on your core and flexibility with PiYo.

The HIIT Bootcamp/Kickboxing class is a great option for students focused on a high intensity cardio, strength, and core conditioning workout with kickboxing moves. If you are drawn to cardio dance, WERQ is for you! This wildly addictive cardio dance class is based on the hottest pop and hip hop music. The workout is nonstop with repetitive athletic moves and fresh dance steps.

Physical education classes and participation in intercollegiate athletics carry one-half semester hour of elective credit. One semester hour of credit may be applied to graduation. The following courses are available each semester:

### First Year Seminar – 3 credit hours

### Communications – 6 credit hours

### Social and Behavioral Sciences – 9 credit hours

- PSYC 101- General Psychology (3 credits)
- PSYC 233- Lifespan Development for Nurses (3 credits)
- SOC 201 The Sociological Imagination (3 credits)

### History – 3 credit hours

- HGP 110 – Development of Civilization (3 credits) OR
- HGP 111 – Development of Civilization (3 credits) OR
- HIST 202 – American History to 1865 (3 credits) OR
- HIST 203 – American History to Present (3 credits)
- POL 291 – American Government (3 credits)

### Arts and Humanities – 3 credit hours (Select one)

- ART 101 Art and Creativity (3 credits)
- ART 103 Art Appreciation (3 credits)
- ENG 203 Major Themes in Literature (3 credits)
- MUS 100 Introduction to Music Literature (3 credits)
- THTR 180 Introduction to Theatre (3 credits)
- PHIL 201 Introduction to Philosophy (3 credits)
- PHIL 205 Logic (3 Credits)
- COM 255 Fundamentals of Media Communication (3 credits)

### Quantitative Thinking – 7 credit hours

- PSYC 211 Intro to Statistics (with Lab) (4 credits) –
**Required** - Grade of C or Better (C- is not acceptable)
- MATH 104 Finite Mathematics (3 credits)
- MATH 106 College Algebra (3 credits) –
**Recommended** - MATH 120 Single Variable Calculus I (5 credits)

### Science Foundations and Issues – 19 credit hours

Grade of C or better is required for the following courses (C- is not acceptable)

- BIOL 125 Nutrition (3 credits)
- BIOL 205 Anatomy and Physiology I (with Lab) (4 credits)
- BIOL 206 Anatomy and Physiology II (with Lab) (4 credits)
- BIOL 215 Microbiology for Non-Majors (with Lab) (4 credits)
- CHEM 105 Intro General, Organic & Bio Chem (4 credits)
- CHEM 105L Intro General, Organic & Bio Chem Lab (1 credit)

No online classes will be accepted for BIOL 205, BIOL 206, BIOL 215, CHEM 105 and CHEM 105L

All Pre-Requisite Courses Must Be Completed Before Entering the Nursing Program

Minimum grade of C- or better unless otherwise noted is required for all courses

### Nursing

Richardson Hall

Nursing Department, Suite 2250

208 Edgemont Blvd.

Alamosa, CO 81101

## Area V. Physical and Natural Sciences

### 7 Credits

- BIOL 101 – Introductory Biology (GT-SC1) 4 credits
- BIOL 125 – Nutrition (GT-SC2) 3 credits
- BIOL 209 – General Biology with Lab (GT-SC1) 5 credits
- BIOL 210 – General Biology with Lab (GT-SC1) 5 credits
- CHEM 103 – Intro to Forensic Chemistry (GT-SC1) 4 credits
- CHEM 111 – Introductory Chemistry with Lab (GT-SC1) 5 credits
- CHEM 131 – General Chemistry with Lab (GT-SC1) 5 credits
- CHEM 132 – General Chemistry with Lab (GT-SC1) 5 credits
- ENV 101 – Introduction to Environmental Science (GT-SC1) 4 credits
- GSCI 109 – Dynamic Earth (GT SC1) 4 credits
- PHYS 110 – Astronomy: Stars & Galaxies (GT-SC2) 3 credits
- PHYS 225 – College Physics I with Lab (GT-SC1) 5 credits
- PHYS 230-231 – General Physics I with Lab (GT-SC1) 5 credits
- PHYS 232-233 – General Physics II with Lab (GT-SC1) 5 credits

One credit hour must be a lab.