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Mathematical Sciences

Department of Mathematical Sciences

http://www.math.montana.edu/

The Department of Mathematical Sciences has programs leading to the Bachelor of Science, the Master of Science, and the Doctor of Philosophy degrees. The B.S. options in mathematics, applied mathematics, statistics, and teaching are listed below.

Many undergraduate courses are sufficiently basic to be of general interest. Detailed and current information on undergraduate course offerings is available from the department.

The four-year baccalaureate curriculum in mathematics is flexible and can accommodate students desiring to concentrate in mathematics, applied mathematics, mathematics teaching, or statistics. Programs in these concentrations are designed with the help of faculty advisors.

Mathematics Option

The mathematics option prepares students for graduate work in mathematics. The core of the program is built around three years of analysis, as well as courses in abstract and linear algebra. The program is flexible enough to accommodate students who wish to prepare for employment in business, industry, or government as technical analysts or specialists in the area of scientific computing. The core mathematics curriculum taken in conjunction with a secondary emphasis in other subject matter areas will prepare a student for employment as an analyst or computational specialist in those areas.

Applied Mathematics Option

Applied mathematicians learn to describe physical phenomena using deterministic models. These models are applicable to the biological and physical sciences and the student is trained to use differential equations, mathematical analysis and computational science to draw insights into various exciting fields.

Applied mathematics is primarily designed to prepare graduates for employment in business, industry, and government. However, an appropriate choice of electives can ensure the student a solid preparation for graduate work in mathematics, statistics, or scientific computing. The program demonstrates the utility of mathematics to solve problems arising in real industrial applications. Graduates will be qualified for professional careers in computational applications of mathematics, statistics, and other related fields.

Mathematics Teaching Option

The teaching option in the mathematics curriculum is designed specifically to prepare students to teach mathematics at the middle school or high school levels. The program includes the mathematics courses for a teaching major and the necessary courses in education which qualify the student for teacher's certification.

Students must consult with an advisor before selecting single or multiple endorsement. Most students opt for multiple subject endorsement, in which case they will complete a teaching minor in an area of their choice. When approved by an advisor, students may opt for a single endorsement in mathematics, in which case they take advanced coursework in mathematics instead of a minor.

Statistics Option

Statisticians are trained in principles of quantitative reasoning. They learn how to discover patterns in data, how to display data, how to construct mathematical models for data, and how to detect biases and uncertainties in data summaries or models. They are trained to design and analyze observational studies, surveys, and scientific experiments. The computer is an essential tool for statistical work.

Statisticians are in demand; successful students should find that job opportunities are excellent. Although positions are available nationwide, the best employment opportunities are found in urban areas, industrial sites, and centers of government. The statistics option prepares students for such positions or for entry into a graduate program in statistics.


Curricula in Mathematics


MATHEMATICS OPTION

M 171 (or M 181), 172 (or M 182), 221, 273 (or M 283), 274 (or M 284), 242, 333, 381, 382, 431 and STAT 332 are required.

In addition, 15 credits from the following math or stat electives list are required: M 330, 348, 349, 386, 430, 441, 422, 450, 451, 454, 455, 472; STAT 421 and STAT 422. Six of these fifteen credits must be from M 430, 441, 442, 450, 451, 454, 455, and 472.

PHSX 220 and 222 are required. However, with the agreement of the student's advisor, PHSX 222 may be replaced with a course in another mathematical application area.

A minimum of 120 credits is required for graduation; 42 of these credits must be in courses numbered 300 and above. Core 2.0 must be completed for graduation.

Freshman Year F S
CLS 101US--Knowledge and Community     3
WRIT 101W--College Writing      3
Choose one of the two:
     M 171Q--Calculus I    4
     M 181Q--Honors Calculus I    4
Choose one of the two:
     M 172Q--Calculus II    4
     M 182Q--Honors Calculus II    4
PHSX 220--Physics I     4  
PHSX 222--Physics II       4
University Core and Electives     4 4
15 15
Sophomore Year F S
M 221--Introduction to Linear Algebra     3
Choose one of the two:
     M 273Q--Multivariable Calculus    4
     M 283Q--Honors Multivariable Calculus    4
Choose one of the two:
     M 274--Intro to Differential Equations    4
     M 284--Honors Intro to Diff Equations    4
M 242--Methods of Proof      3  
STAT 332--Stat for Scientists & Engineers 3
University Core and Electives     8 4
15 14
Junior Year F S
M 333--Linear Algebra    3
M 381--Advanced Calculus I     3
M 382--Advanced Calculus II     3
Math or Stat Elect (See List Above)     3 3
University Core and Electives     6 9
15 15
Senior Year F S
M 431--Abstract Algebra I    3
Math or Stat Elect (See List Above)     6 3
University Core and Electives     9 10
15 16

APPLIED MATHEMATICS OPTION

M 171 (or M 181), 172 (or M 182), 221, 273 (or M 283), 274 (or M 284), 242, 348, 349, 386, 441, 442 and STAT 332 are required.

In addition, 12 credits from the following math or stat electives list are required M 330, 333, 381, 382, 430, 431, 450, 451, 454, 455, 472, STAT 421 and STAT 422. Six of these 12 credits must be from M 430, 450, 451, 454, 455.

PHSX 220, 222, and 224 are required. However, with the agreement of the student's advisor, PHSX 224 may be replaced by PHSX 301, or both PHSX 222 and PHSX 224 may be replaced by a two-course sequence in another mathematical application area.

A minimum of 120 credits is required for graduation; 42 of these credits must be in courses numbered 300 and above. Core 2.0 must be completed for graduation.

Freshman Year F S
Choose one of the two:
     CLS 101US--Knowledge and Community     3
     COM 110US--Public Communication    3
WRIT 101W--College Writing I      3
Choose one of the two:
     M 171Q--Calculus I     4
     M 181Q--Honors Calculus I     4
Choose one of the two:
     M 172Q--Calculus II     4
     M 182Q--Honors Calculus II     4
PHSX 220 --Physics I     4  
PHSX 222 --Physics II       4
University Core and Electives     4 4
15 15
Sophomore Year F S
M 221--Introduction to Linear Algebra     3
Choose one of the two:
     M 273Q--Multivariable Calculus     4
     M 283Q--Honors Multivariable Calculus     4
Choose one of the two:
     M 274--Intro to Differential Equations     4
     M 284--Honors Intro to Diff Equations     4
M 242--Methods of Proof      3
PHSX 224--Physics III     4  
University Core and Electives     4 8
15 15
Junior Year F S
M 348 --Techniques of Applied Mathematics I    3
M 349 --Techniques of Applied Mathematics II  3
M 386R --Software Applications in Math  3
STAT 332--Stat for Scientists & Engineers     3
Math or Stat Elect (See List Above)     3 3
University Core and Electives     6 6
15 15
Senior Year F S
M 441--Numerical Linear Algebra and Optimization    3  
M 442--Numerical Solution of Differential Equations    3
Math or Stat Elect (See List Above)     3 3
University Core and Electives     9 9
15 15

STATISTICS OPTION

M 171, 172, 221, 273, 242, and either 333 or 441 are required. STAT 408, 410, 412, 421, 422, 446, and either STAT 332 or STAT 217 are required (STAT 217 requires STAT 216 or equivalent as a prerequisite).

In addition, 15 credits from the following math or stat electives list are required: STAT 431, 436, 437, 439, 448, 490 or 491. Other courses approved by an advisor may be substituted. At least one science must have a lab.

A minimum of 120 credits is required for graduation; 42 of these credits must be in courses numbered 300 and above. Core 2.0 must be completed for graduation.

Freshman Year F S
Choose one of the two:
     CLS 101US--Knowledge and Community   3
     COM 110US--Public Communication    3
WRIT 101W--College Writing I    3
M 171Q--Calculus I     4
M 172Q--Calculus II     4
University Core and Electives     8 9
15 16
Sophomore Year F S
M 221--Introduction to Linear Algebra    3
M 273Q--Multivariable Calculus     4
Choose one of the two:
     STAT 217Q--Intermed Stat Concept     3  
     STAT 332--Stat-Scientist & Engineers    3
STAT 408 --Stat Computing & Grph Analysis    3
M 242--Methods of Proof    3  
Science Electives    4 3
University Core and Electives       6
14 15
Junior Year F S
Choose one of the two:
     M 333 --Linear Algebra 3
     M 441--Num Linear Alg & Optimization     3
STAT 411--Data Analysis I     3
STAT 412--Data Analysis II       3
STAT 446--Sampling     3
Math or Stat Elect (See List Above)    3
Science Electives     3 3
University Core and Electives     3 6
15 15
Senior Year F S
STAT 421--Probability Theory     3
STAT 422--Mathematical Stat     3
Math or Stat Elect (See List Above)     6 6
University Core and Electives     6 6
15 15

Actuary Profession Bound Students

Actuary profession-bound students are advised to take STAT 421 and STAT 422 during the junior year in order to be prepared for the actuarial exams given during the senior year. For further guidance, see the Actuary Advisor in the Dept. of Mathematical Sciences, 2-214 Wilson Hall.


MATHEMATICS TEACHING OPTION

M 171, 172, 273, 274, 242, 328, 329, 428 and STAT 332 are required. PHSX 205 is required as a science course.

For a multiple subject endorsement, six additional credits of electives in mathematics are required. These credits may be chosen from M 221 or any other mathematics or statistics course numbered 300 or above. A teaching minor is required.

For a single subject endorsement in mathematics, M 221 and either M 381 or M 431 are required. In addition, nine credits of electives are required. These credits may be chosen from any mathematics or statistics course numbered 300 or above.

Multiple Subject Endorsement

Freshman Year F S
Choose one of the two:
     CLS 101US--Knowledge and Community 3
     COM 110US--Public Communication    3
EDU 202--Early Field Experience    1
WRIT 101W--College Writing I    3
Choose one of the two:
     HDCF 150IS--Lifespan Human Dev    3
     EDEC 160--Early Childhood through Adolescent Development 3
M 171Q--Calculus I     4
M 172Q--Calculus II     4
University Core, Minor, & Electives     6 8
16 16
Sophomore Year F S
EDU 223--Ed Psy & Adolescent Dev 3
EDU 211D--Multicultural Education     3
EDU 370--Integrating Tech into Education       2
M 273Q--Multivariable Calculus     4
M 274--Intro to Differential Equation     4
M 242--Methods of Proof     3
PHSX 205--College Physics I     4
University Core, Minor, & Electives     5 3
16 15
Junior Year F S
EDU 382--Assessment, Curric, Instruction     3
EDU 497R--Methods: 5-8 Mathematics      3
HDCF 356--Exceptional Children     3
M 328--Higher Math for Sec Teachers     3
M 329--Modern Geometry     3
STAT 332--Stat for Scientists & Engineers    3
Math/Stat(300+) or M 221     3
University Core, Minor, & Electives     6 3
15 15
Senior Year F S
EDU 395--Practicum: 5-12      3
EDU 495--Student Teaching: 5-12    10
EDU 408--Professional Issues: 5-12     2
EDU 497--Methods: 9-12 Mathematics     3
M 428--Math Modeling for Teachers     3
Math/Stat(300+) or M 221         3
University Core, Minor, & Electives     3
15 12

Single Subject Endorsement

Freshman Year F S
Choose one of the two:
     CLS 101US--Knowledge and Community    3
     COM 110US--Public Communication    3
EDU 202--Early Field Experience    1
WRIT 101W--College Writing I      3
Choose one of the two :
     HDCF 150IS--Lifespan Human Dev    3
     EDEC 160--Early Childhood through Adolescent Development 3
M 171Q--Calculus I     4
M 172Q--Calculus II     4
PHSX 205--College Physics I      4
University Core and Electives     5 3
15 15
Sophomore Year F S
EDU 223--Ed Psy & Adolescent Dev     3
EDU 211D--Multicultural Education     3
EDU 370--Integrating Tech into Education     2
M 221--Introduction to Linear Algebra     3
M 273Q--Multivariable Calculus     4
M 274--Intro to Differential Equations     4
M 242--Methods of Proof     3
STAT 332--Stat for Scientists & Engineers     3
University Core and Electives     3 3
15 16
Junior Year F S
EDU 382--Assessment, Curric, Instruction     3
EDU 497R--Methods: 5-8 Mathematics      3
HDCF 356--Exceptional Children     3
M 328--Higher Math for Sec Teachers     3
M 329--Modern Geometry     3
Choose one of the two:  
     M 381--Advanced Calculus I 3
     M 431--Abstract Algebra I   (3)
Math/Stat(300+)     3 3
University Core and Electives     4 4
16 16
Senior Year F S
EDU 395--Practicum: 5-12      3
M 428--Math Modeling for Teachers     3
EDU 497--Methods: 9-12 Mathematics      3
EDU 408--Professional Issues: 5-12     2
EDU 495--Student Teaching: 5-12    10
Math/Stat(300+)     3
University Core and Electives     3
15 12

MATHEMATICS MINOR (NON-TEACHING)

Credits
M 171Q--Calculus I    4
M 172Q--Calculus II     4
M 221--Introduction to Linear Algebra     3
M 273Q--Multivariable Calculus     4
M 274--Intro to Differential Equation      4
Nine credits from the following:
     M 330--History of Mathematics     3
     M 333--Linear Algebra     3
     M 348--Techniques of Applied Math I     3
     M 349--Techniques of Applied Math II     3
     M 381--Advanced Calculus I     3
     M 382--Advanced Calculus II     3
     M 386R--Software Applications in Math     3
     M 430--Math Biology     3
     M 431--Abstract Algebra I     3
     M 441--Num Linear Alg & Optimization     3
     M 442--Num Solution of Diff Equations     3
     M 450--Applied Mathematics I     3
     M 451--Applied Mathematics II     3
     M 454--Intro to Dynamical Systems I     3
     M 455--Intro to Dynamical Systems II     3
     M 472--Intro to Complex Analysis     3
     STAT 421--Probability Theory     3
     STAT 422--Mathematical Statistics     3
28

STATISTICS MINOR (NON-TEACHING)

Choose one of the two:             Credits
     STAT 217Q--Intermed Stat Concept             3
     STAT 332--Stat for Scientists & Engineers             3
Eight credits of Math (171 or higher)             8
Twelve credits of STAT (408 or higher)             12
23

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