Mathematics Education
Individuals interested in teaching in K12 schools must complete a degree in the content area they want to teach plus the teacher preparation program through the Department of Curriculum and Instruction. Individuals must complete the teaching major/teaching track within that degree program, which may contain different course requirements than the academic major since the sequence of courses is designed to meet state standards. Upon completion of the degree program with the teaching track and the secondary licensure program, one will be eligible for a standard Montana teaching license in this content area.
Bachelor of Arts  Mathematics; Mathematics Education Option
College Humanities & Sciences
Catalog Year: 20162017
Degree Specific Credits: 53
Required Cumulative GPA: 2.5
Note: (1) The number of degree specific credits required is significantly higher if one also counts the additional course work required by the Teacher Education Program.
(2) Note that the Teacher Education Program requires in addition an overall cumulative GPA of at least 2.75.
Mathematical Sciences Courses Required for the Mathematics Education Option
Rule: The courses in this category must be completed with a cumulative GPA of at least 2.75.
Calculus I
Rule: Take 1 of the following 2 courses.
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M 171  Calculus I
Offered autumn and spring. Prereq., M 122 or 151 or ALEKS placement >= 5. Differential calculus, including limits, continuous functions, Intermediate Value Theorem, tangents, linear approximation, inverse functions, implicit differentiation, extreme values and the Mean Value Theorem. Integral Calculus including antiderivatives, definite integrals, and the Fundamental Theorem of Calculus.

4 Credits 
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M 181  Honors Calculus I
Offered autumn. Prereq., consent of instr. Coreq., Honors Calculus Seminar, a section of M 294. Honors version of M 171.

4 Credits 
Minimum Required Grade: C  4 Total Credits Required 
Calculus II
Rule: Take 1 of the following 2 courses.
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M 172  Calculus II
Offered autumn and spring. Prereq., M 171 or 181. Techniques of Integration. Area computations. Improper integrals. Infinite series and various convergence tests. Power series. Taylor's Formula. Polar coordinates. Parametric curves.

4 Credits 
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M 182  Honors Calculus II
Offered spring. Prereq., M 181 or consent of instr. Coreq., Honors Calculus Seminar, a section of M 294. Honors version of M 172.

4 Credits 
Minimum Required Grade: C  4 Total Credits Required 
Other Mathematical Sciences Core Courses for the Mathematics Education Option
Rule: Take all of the following courses.
Note: (1) Residency Requirement: At least 4 of the upperdivision courses in this category must be taken at UMMissoula (only 3 if the Elective Course is an upperdivision course taken at UMMissoula).
(2) Note that taking M 429 satisfies the Advanced College Writing Requirement for this degree.
(3) STAT 451 can be substituted for STAT 341, if STAT 451 is not selected as the elective course.
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M 221  Introduction to Linear Algebra
Offered autumn and spring. Prereq., M 172 or 182. Vectors in the plane and space, systems of linear equations and Gauss–Jordan elimination, matrices, determinants, eigenvalues and eigenvectors, vector spaces, linear transformations. Calculators and/or computers used where appropriate.

4 Credits 
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M 301  Math Technology for Teachers
Offered autumn. Prereq., M 221. Discrete and continuous mathematical models from a variety of disciplines using appropriate technology.

3 Credits 
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M 307  Intro to Abstract Mathematics
Offered autumn and spring. Prereq., M 172 or 182. Designed to prepare students for upper–division proof–based mathematics courses. Topics include proof techniques, logic, sets, relations, functions and axiomatic methods. Students planning to take both M 221 and 307 are encouraged to take M 221 first.

3 Credits 
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M 326  Number Theory
Offered spring. Prereq., M 225 or 307. Congruences, Diophantine equations, properties of primes, quadratic residues, continued fractions, algebraic numbers.

3 Credits 
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M 429  History of Mathematics
Offered spring. Prereq., M307. Historical study of the development of mathematics from the Egyptian and Babylonian eras to the 20th century. Level: UndergraduateGraduate

3 Credits 
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M 431  Abstract Algebra I
Offered autumn. Prereq., M 221 and 307 or consent of instr. An introduction to modern ideas of algebra through the study of groups, rings, and fields. Level: UndergraduateGraduate

4 Credits 
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M 439  Euclidean & NonEuclidean Geo
Offered autumn. Prereq., M 307. Euclidean geometry from a rigorous, axiomatic viewpoint and Non–Euclidean geometries chosen from Lobachevskian, projective, finite and Riemannian. Level: UndergraduateGraduate

3 Credits 
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STAT 341  Intro to Probability and Stat
Offered autumn and spring. Prereq., one of M 162, 172 or 182. Probability, probability models and simulation, random variables, density functions, special distributions, and a brief survey of estimation and hypothesis testing. Computer use integrated throughout.

3 Credits 
Minimum Required Grade: C  26 Total Credits Required 
Elective Course
Rule: Take one of the following:
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M 273  Multivariable Calculus
Offered autumn and spring. Prereq., M 172 or 182. Calculus of functions of several variables; differentiation and elementary integration. Vectors in the plane and space.

4 Credits 
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M 311  Ordinary Diff Equations/System
Offered autumn. Prereq., M 273. Ordinary differential equations. Systems of linear differential equations from a matrix viewpoint. Series solutions. Existence and uniqueness for initial value problems. Numerical methods. Stability and selected topics. M 317 computer lab recommended.

3 Credits 
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M 325  Discrete Mathematics
Offered spring. Prereq., M 171 and 225 or 307. Continuation of 225 and topics from graph theory, Boolean algebras, automata theory, coding theory, computability and formal languages.

3 Credits 
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M 361  Discrete Optimization
Offered spring. Prereq., one of M 162, 172 or 182 (221 or 225 recommended). Intended for non–mathematics majors as well as mathematics majors. Introduction to discrete optimization and modeling techniques with applications. Topics from combinatorics and graph theory, including enumeration, graph algorithms, matching problems and networks.

3 Credits 
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M 362  Linear Optimization
Offered autumn. Prereq., one of M 162, 172 or 182 (221 recommended). Coreq., M 363 recommended. Intended for non–mathematics majors as well as majors. Introduction to linear programming and modeling techniques with applications. Topics include the simplex method, duality, sensitivity analysis and network models.

3 Credits 
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M 381  Advanced Calculus I
Offered autumn . Prereq., M 307. Rigorous development of singlevariable calculus with formal proof. Functions, sequences, limits, continuity, differentiation, and integration.

3 Credits 
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M 412  Partial Differential Equations
Offered spring. Prereq., M 311. Fourier series, Sturm–Liouville and boundary value problems. Partial differential equations: Cauchy problems and the method of characteristics, separation of variables and Laplace transform methods. Numerical methods and selected topics. M 418 computer lab recommended. Level: UndergraduateGraduate

3 Credits 
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M 414  Deterministic Models
Offered spring. Prereq., M 263 or 311 or consent of instr. Linear and nonlinear difference and differential equations: stability, phase–plane analysis, oscillatory behavior, limit cycles, and chaos. Eigenvalues and eigenfunctions. Emphasis on models in biology. Level: UndergraduateGraduate

3 Credits 
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M 432  Abstract Algebra II
Offered spring. Prereq., M 431. Continues the investigation of groups, rings, and fields begun in M 431. Further topics include vector spaces and field extensions. Level: UndergraduateGraduate

4 Credits 
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M 440  Numerical Analysis
Offered intermittently. Prereq., 311, one computer language. Error analysis; approximation and interpolation, numerical solution of linear and nonlinear equations, numerical integration of ordinary and partial differential equations. Level: UndergraduateGraduate

4 Credits 
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M 445  Stat/Math/Comp Modeling
Offered autumn oddnumbered years. Prereq., consent of instr. An interdisciplinary course on the integration of statistical and dynamical models with applications to biological problems. Linear and nonlinear models, estimation, systems of ordinary differential equations, numerical integration, bootstrapping, MCMC methods. Intended both for students in mathematics and the natural sciences. Level: UndergraduateGraduate

4 Credits 
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M 461  Practical Big Data Analytics
Offered autumn. Prereq., STAT 341, and one of M 221 or M 273, or consent of instructor. This is a methods course supporting the Big Data Certificate Program. The course provides the students with the essential tools for the analysis of big data. The content consists of map reduce and canonical information methods for analyzing massively large data sets, windowing methods for the analysis of streaming data, an introduction to predictive analytics, and an introduction to data visualization methods. Level: UndergraduateGraduate

3 Credits 
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M 462  Theoretical Big Data Analytics
Offered spring. Prereq., M 221 and two other Mathematics / Statistics classes at the 200level or above, or consent of instr. The main goal of this course is to provide students with a unique opportunity to acquire conceptual knowledge and theoretical background behind mathematical tools applicable to Big Data Analytics and Real Time Computations. Specific challenges of Big Data Analytics, e.g., problems of extracting, unifying, updating, and merging information, and processing of highly parallel and distributed data, will be reviewed. The tools for Big Data Analytics, such as regression analysis, linear estimation, calibration problems, real time processing of incoming (potentially infinite) data, will be studied in more detail. It will be shown how these approaches can be transformed to conform to the Big Data demands. Level: UndergraduateGraduate

3 Credits 
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M 472  Intro to Complex Analysis
Offered spring. Prereq., M 273, M 307. Analytic functions, complex integration, singularities and application to contour integration, harmonic functions, spaces of analytic functions. Level: UndergraduateGraduate

4 Credits 
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M 473  Introduction to Real Analysis
Offered autumn oddnumbered years. Prereq., M 273, M 307. Theory of metric spaces and point set topology, RiemannStieltjes integral, sequences and series of functions. StoneWeierstrass theorem, theorem of ArzelaAscoli, introduction to Lebesgue integration. Level: UndergraduateGraduate

4 Credits 
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M 485  Graph Theory
Offered autumn. Prereq., M 325, or M 307 and M 361, or consent of instr. Theory and applications of graphs. Topics chosen from trees, matchings, connectivity, coloring, planarity, Ramsey theory, random graphs, combinatorial designs and matroid theory. Level: UndergraduateGraduate

3 Credits 
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STAT 421  Probability Theory
Offered autumn. Prereq., M 273 or consent of instructor (STAT 341 recommended). An introduction to probability, random variables and their probability distributions, estimation and hypothesis testing. This course is the foundation on which more advanced statistics courses build. Level: UndergraduateGraduate

3 Credits 
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STAT 422  Mathematical Statistics
Offered spring. Prereq., STAT 421. Continuation of 421. Level: UndergraduateGraduate

3 Credits 
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STAT 451  Statistical Methods I
Offered autumn. Prereq., one year of college mathematics including M 115 or equiv. course in probability or consent of instr. May not be counted toward a major in mathematics. Intended primarily for nonmathematics majors who will be analyzing data. Graphical and numerical summaries of data, elementary sampling, designing experiments, probability as a model for random phenomena and as a tool for making statistical inferences, random variables, basic ideas of inference and hypothesis testing. Level: UndergraduateGraduate

3 Credits 
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STAT 452  Statistical Methods II
Offered spring. Prereq., STAT 451. Continuation of STAT 451. May not be counted toward a major in mathematics. Multiple regression, experimental design, analysis of variance, other statistical models. Level: UndergraduateGraduate

3 Credits 
Minimum Required Grade: C  34 Total Credits Required 
Mathematics Teaching Methods Course
Rule: Take the following course.
Note: The course number EDU 497 covers many different teaching methods courses. The section of EDU 497 entitled "Methods: 5  12 Mathematics" is required for the Mathematics Education option.
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EDU 497  Teaching and Assessing
(R15) Offered autumn and/or spring. Prerequisite: Admission to the Teacher Education Program. This course number is used for multiple elementary and secondary methods courses. Check the class schedule or with your advisor regarding appropriate sections.
58 Mathematics: 3 cr. Offered autumn and spring. This class must be taken concurrently with Level 3 courses and is restricted to students who have completed coursework in Levels 1 & 2. Methods of teaching, assessing, and evaluating mathematics in the 58 middle grades including number and operations, rational numbers, ratio and proportion, measurement, algebra, expressions and equations, geometry, probability, statistics, and functions.
K8 Social Studies: 3 cr. Offered autumn and spring. This class must be taken concurrently with Level 3 courses and is restricted to students who have completed coursework in Levels 1 & 2. Emphasis on developing teaching and assessing social studies teaching/learning opportunities that incorporate literature, primary sources and other developmentally appropriate activities. Overarching themes address diversity, integration across the curriculum and understanding state and national curriculum standards.
K8 Science: 3 cr. Offered autumn and spring. This class must be taken concurrently with Level 3 courses and is restricted to students who have completed coursework in Levels 1 & 2. Emphasis on developing, teaching, and assessing science teaching/learning opportunities that are inquirybased, developmentally appropriate, integrated across the curriculum, and aligned with state and national curriculum standards.
48 Reading: 3 cr. Offered autumn and spring. This class must be taken concurrently with Level 3 courses and is restricted to students who have completed coursework in Levels 1 & 2. Preparation for teaching reading in a 48 setting so that all students are successful. Emphasis on reading to learn. Focus on using assessment to guide instruction, learning from trade books, textbooks, and electronic texts, activating prior knowledge, studying texts, and developing student enthusiasm for reading.
512 Science: 3 cr. Offered autumn. Methods of teaching science in the middle and secondary school. This course emphasizes the use of inquiry, problemsolving, appropriate use of technology, and assessment techniques that align with state and national curriculum standards.
512 Social Studies: 3 cr. Offered autumn. Foundations and purpose of the middle and secondary social studies curriculum. Elements of curricular design, including instructional methods, materials and assessment.
512 Mathematics: 4 cr. Offered autumn. Methods for teaching mathematics in grades 512 focusing on presentation of mathematics concepts and procedures through models, problem solving, and technology. Development of instructional strategies and classroom organizational models, discourse in the classroom, and multiple means for assessing student progress.
512 Business Subjects: 4 cr. Offered autumn. Methods for teaching business subjects in grades 512 focusing on contentspecific topics in business, marketing, and information technology to include: instructional planning; effective teaching strategies (F2F & online); multiple means for assessing student progress; classroom management; and the relationship of the content area to standardsbased curricula.

0 To 4 Credits 
Minimum Required Grade: C  4 Total Credits Required 
Science Requirement for the Mathematics Education Option
Rule: Take 12 credits in at most two areas selected from astronomy (ASTR), biology (BIO*), chemistry (CHMY), computer science (CSCI, except CSCI TR*), economics (ECNS), forestry (FORS, WILD), geosciences (GEO), management information systems (BMIS), and physics (PHSX).
Note: (1) Students completing a teaching minor (in another subject) or a second major are exempt from this requirement.
(2) Transfer courses listed on the transcript as “CSCI TR*” may include course work in other areas such as Computer Applications (CAPP) and therefore do not count towards this requirement unless a student successfully petitions the Department of Mathematical Sciences.
Secondary Teaching Licensure
Note: For licensure to teach mathematics, a student must also gain admission to the Teacher Education Program and meet all the requirements for secondary teaching licensure (see the College of Education and Human Sciences).