# The Department of Mathematics

**Dr. Mark Jacobson, Chair**

LA 848, (406) 657-2228

**mjacobson@msubillings.edu**

The mathematics major is designed to include students with a wide variety of goals and backgrounds. Mathematics is an excellent preparation for fields from technical to legal, from scientific to managerial, and from computational to philosophic. It is also a source of pleasure and satisfaction for people in every line of endeavor. Therefore, MSU Billings’ programs are constructed to welcome interested students of all sorts. Our programs reflect the diversity of interests of our students and the increasingly diverse nature of the mathematical sciences.

## Advising Information

Students are encouraged to meet with their advisor each semester to confirm that their plan of study is accurate and complete. If necessary, changes and updates should be made in order to ensure that program requirements can be completed in a timely manner. Faculty advisors work with students to explore appropriate internships, cooperative education placements and/or experiential learning opportunities which will enhance the student’s academic program. In addition, advisors provide assistance in selecting elective courses which support the student’s interests, career plans and plan of study.

Academic advising services for all freshmen Arts and Sciences majors are provided through Advising & Career Services on McMullen Hall first floor west. Upon declaring a specific major, Arts and Science majors will be assigned to a faculty advisor in their department for upper-division advising. Advising files for all upper-division students are maintained in the departmental office of the program in which the student is majoring. Although advisors are available to assist students in designing their Plans of Study, students are ultimately responsible for meeting degree requirements.

## Learning Outcomes for Math Department

- Demonstrate proficiency in geometry, algebra, calculus, mathematical analysis, probability and statistics, and discrete mathematics.
- Read, comprehend, critique, and construct rigorous mathematical arguments and proofs.
- Effectively use technology such as (but not limited to) computer algebra systems, statistical software, and calculators to solve, analyze, or explore mathematics problems.
- Demonstrate effective communication of mathematics through collaborative projects and presentations.

Code | Title | Credits |
---|---|---|

1. | ||

Geometry | ||

M 329 | Modern Geometry | 3 |

Algebra | ||

M 333 | Linear Algebra | 4 |

M 431 | Abstract Algebra I | 3 |

Calculus | ||

M 171 | Calculus I | 4 |

M 172 | Calculus II | 4 |

M 273 | Multivariable Calculus | 4 |

M 274 | Intro Differential Equations | 4 |

Mathematical analysis | ||

M 471 | Mathematical Analysis | 3 |

M 472 | Intro to Complex Analysis | 3 |

Probability and statistics | ||

STAT 341 | Intro Probability & Statistics | 4 |

Discrete mathematics | ||

M 305 | Discrete Structures I | 4 |

2. | ||

M 242 | Methods of Proof | 3 |

M 329 | Modern Geometry | 3 |

M 431 | Abstract Algebra I | 3 |

M 471 | Mathematical Analysis | 3 |

STAT 341 | Intro Probability & Statistics | 4 |

M 305 | Discrete Structures I | 4 |

M 499 | Capstone | 3 |

3. | ||

M 110 | Mathematical Computing | 1 |

CSCI 111A | Programming with Java I | 4 |

M 305 | Discrete Structures I | 4 |

M 274 | Intro Differential Equations | 4 |

M 333 | Linear Algebra | 4 |

M 305 | Discrete Structures I | 4 |

STAT 341 | Intro Probability & Statistics | 4 |

M 431 | Abstract Algebra I | 3 |

M 371 | Numerical Computing | 4 |

M 499 | Capstone | 3 |

4. | ||

STAT 341 | Intro Probability & Statistics | 4 |

M 499 | Capstone | 3 |

## Computer Science

**COMP 100 Topics in Comp Prog. 3 Credits**

Prerequisite(s): M 095 or equivalent.

R-9. Introduces the logic and techniques of computer programming. Computer languages will vary; may be repeated for credit when different languages are offered. Possible topics include BASIC, LOGO or Introductory Pascal.

Lecture Hours 3

Department: Math/Comp Sci/Statistics

**COMP 292 Seminar. 1-3 Credits**

Provides students an opportunity to investigate topics pertinent to the field of Computer Science.

Department: Math/Comp Sci/Statistics

**COMP 293 Workshop. 1-8 Credits**

Provides an opportunity for experimental study in an area of Computer Science.

Department: Math/Comp Sci/Statistics

**COMP 311 Digital Logic Design. 3 Credits**

Prerequisite(s): CSCI 132.

Corequisite(s): COMP 312.

Covers number representation, fundamental codes, concepts of Boolean algebra, basic logic algorithms, arithmetic, logic units, and computer architecture.

Lecture Hours 3

Department: Math/Comp Sci/Statistics

**COMP 312 Logic Design Lab. 2 Credits**

Prerequisite(s): PHSX 205.

Corequisite(s): COMP 311.

Covers digital logic circuit design with software assistance. Hands-on experience in the design and construction of digital logic circuits. (Lab fee required.)

Lab Hours 2

Department: Math/Comp Sci/Statistics

**COMP 390 Practicum. 1 Credit**

Prerequisite(s): CSCI 246.

Provides practical experience in the administration of a desktop laboratory. Includes both hardware and software troubleshooting.

Department: Math/Comp Sci/Statistics

**COMP 402 Artificial Intelligence. 3 Credits**

Prerequisite(s): CSCI 246 and some programming experience.

Covers data representation, production systems, search strategies, expert systems. Leads to competence with an AI language such as LISP.

Lecture Hours 3

Department: Math/Comp Sci/Statistics

**COMP 491 Independent Study. 1-5 Credits**

Prerequisite(s): consent of instructor and department chairperson.

Provides outstanding students an individual opportunity to explore material not covered by regular Computer Science courses.

Department: Math/Comp Sci/Statistics

**COMP 492 Seminar. 1-3 Credits**

Prerequisite(s): Mathematics major or minor, or consent of instructor.

Investigates intensively topics pertinent to the area of Computer Science.

Department: Math/Comp Sci/Statistics

**COMP 493 Workshop. 1-3 Credits**

Provides an opportunity for experimental study in an area of Computer Science.

Department: Math/Comp Sci/Statistics

**COMP 496 Cooperative Educ/Internship. 1-3 Credits**

Department: Math/Comp Sci/Statistics

## Computer Science/Programming

**CSCI 111A Programming with Java I. 4 Credits**

Term Typically Offered: Fall, Spring

Prerequisite(s): M 095.

Introduces programming in Java. Presents algorithms and problem solving, data structures in Java, searching and sorting, procedures and functions, and elements of program life cycle.

Lecture Hours 4

Department: Math/Comp Sci/Statistics

**CSCI 132 Bsc Data Structures/Algorithms. 4 Credits**

Prerequisite(s): CSCI 111A. (Sp) Investigates the essential properties of data structures and algorithms for operating on them.

Covers the use of data structures as tools in algorithms design. Provides exposure to searching, sorting, and hashing techniques using the Java language.

Lecture Hours 4

Department: Math/Comp Sci/Statistics

**CSCI 232 Data Structures and Algorithms. 4 Credits**

Computer language Java and software development will be used as the vehicles to introduce applet and its application to computer representations of various important concepts and their applications.

Lecture Hours 4

Department: Math/Comp Sci/Statistics

**CSCI 246 Discrete Structures. 4 Credits**

Prerequisite(s): M 172 and CSCI 111A. (F) Covers logic, recursion, induction and basic data models.

Surveys combinatorics and the theory of algorithms with attention to design analysis and verification techniques.

Lecture Hours 4

Department: Math/Comp Sci/Statistics

**CSCI 260 Object Oriented Programming I. 3 Credits**

Prerequisite: CAPP 131. Familiarizes students with principles of Object-Oriented Programming. Includes Object-Oriented features in selected software packages; creating classes; object hierarchies and collections; Active X components; ADO objects. Juniors will complete a major programming project (Cross-listed with City College).

Lecture Hours 3

Department: College of Business-All Depts

**CSCI 346 Advanced Discrete Structures. 4 Credits**

Term Typically Offered: Spring

Prerequisite(s): CSCI 246.

Discusses algorithm design in the context of graph theory. Introduces automata and formal languages. Covers logic, computability, artificial intelligence and robotics.

Lecture Hours 4

Department: Math/Comp Sci/Statistics

**CSCI 360 Object Oriented Programming II. 3 Credits**

Prerequisite(s): CAPP 131.

Familiarizes students with principles of Object-Oriented Programming. Includes Object-Oriented features in selected software packages; creating classes; object hierarchies and collections; Active X components; ADO objects. Juniors will complete a major programming project (Cross-listed with City College).

Lecture Hours 3

Department: College of Business-All Depts

**CSCI 492 Independent Study. 1-4 Credits**

Department: Math/Comp Sci/Statistics

## Mathematics

**M 105 Contemporary Mathematics. 3 Credits**

Term Typically Offered: Fall, Spring

Prerequisite(s): Appropriate placement score.

Gives students the skills required to understand and interpret quantitative information that they encounter in the news and in their studies, and make numerically based decisions in their lives. Topics include working with units and measurement, set theory, financial mathematics, and essentials of statistics.

Lecture Hours 3

Department: Math/Comp Sci/Statistics

**M 110 Mathematical Computing. 1 Credit**

Term Typically Offered: Fall, Spring

Introduces the use of computer algebra systems to solve mathematical problems.

Lecture Hours 1

Department: Math/Comp Sci/Statistics

**M 121 College Algebra. 3 Credits**

Term Typically Offered: Fall, Spring, Summer

Prerequisite(s): M 095 or M 098 or appropriate placement score.

Covers the concepts of functions, complex numbers, and solving basic system of equations. Investigates linear, quadratic, polynomial, exponential, and logarithmic functions.

Department: Math/Comp Sci/Statistics

**M 122 College Trigonometry. 3 Credits**

Term Typically Offered: Fall, Spring

Prerequisite: M 121 or appropriate placement scores. Covers trigonometric functions and their inverses, polar coordinates, graphing, vectors, and trigonometric identities. Includes sequences and series.

Lecture Hours 3

Department: Math/Comp Sci/Statistics

**M 130 Math for Elementary Teachers I. 3 Credits**

Term Typically Offered: Fall, Spring

Prerequisite(s): M 088 or appropriate placement score.

Stresses topics in counting and cardinality, operations in base ten, basic operations with fractions, rational numbers, two-dimensional geometry, and proportional reasoning. Emphasis is on problem-solving and non-algorithmic thinking within grade K-5 of the Montana Common Core State Standards for mathematics. Designed for majors in elementary education and secondary education.

Lecture Hours 3

Department: Math/Comp Sci/Statistics

**M 131 Math for Elementary Teacher II. 3 Credits**

Term Typically Offered: Fall, Spring

Prerequisite(s): M 130 or consent of instructor.

Stresses advanced operations with fractions, ratios and proportional relationships, analytic and three-dimensional geometry, expressions and equations, and statistics and probability. Emphasis is on problem-solving and non-algorithmic thinking within grades 5-8 of the Montana Common Core State Standards for mathematics.

Lecture Hours 3

Department: Math/Comp Sci/Statistics

**M 143 Finite Mathematics. 4 Credits**

Term Typically Offered: Fall, Spring

Prerequisite(s): M 095 or appropriate placement score.

Studies applications of systems of linear equations to problems of optimization, elementary functions, logic, and mathematics of finance. Introduces differentiation.

Lecture Hours 4

Department: Math/Comp Sci/Statistics

**M 161 Survey of Calculus. 3 Credits**

Term Typically Offered: Fall, Summer

Prerequisite(s): M 121 or appropriate placement test score.

Covers basic calculus concepts including limits, differentiation, and integration with applications to business, science, and social science problems.

Lecture Hours 3

Department: Math/Comp Sci/Statistics

**M 171 Calculus I. 4 Credits**

Term Typically Offered: Fall, Spring

Prerequisite(s): M 122 or appropriate placement score.

Covers differentiation and presents applications to the approximation of functions, root finding, and 1-variable optimization. Introduces integration.

Lecture Hours 4

Department: Math/Comp Sci/Statistics

**M 172 Calculus II. 4 Credits**

Term Typically Offered: Fall, Spring

Prerequisite(s): M 171.

Includes techniques and applications of integration, analytic geometry and the theory of sequences and series. This course is a continuation of M 171.

Lecture Hours 4

Department: Math/Comp Sci/Statistics

**M 242 Methods of Proof. 3 Credits**

Term Typically Offered: Spring

Prerequisite(s): M 172.

Covers reasoning and communication in mathematics, including logic, generalization, existence, definition, proof, and the language of mathematics. Topics include functions, relations, set theory, recursion, algebra, number theory, and other areas of mathematics.

Lecture Hours 3

Department: Math/Comp Sci/Statistics

**M 273 Multivariable Calculus. 4 Credits**

Term Typically Offered: Fall

Prerequisite(s): M 172 and either M 110 or EGEN 105.

Covers vector-valued functions, functions of two and three variables, partial differentiation, as well as multiple, line, and surface integrals; includes a variety of applications.

Lecture Hours 4

Department: Math/Comp Sci/Statistics

**M 274 Intro Differential Equations. 4 Credits**

Term Typically Offered: Spring

Prerequisite(s): M 172 and either M 110 or EGEN 105.

Presents methods for the solution of first and higher-order differential equations including variation of parameters, undetermined coefficients, the Laplace transform, and power series expansions. Introduces phase plane methods.

Lecture Hours 4

Department: Math/Comp Sci/Statistics

**M 294 Seminar/Workshop. 1-8 Credits**

Provides students an opportunity to investigate intensively topics pertinent to the field of Mathematics.

Department: Math/Comp Sci/Statistics

**M 298 Internship/Cooperative Educ. 1-9 Credits**

Provides university credit for a sophomore work experience in the area of Mathematics supervised by faculty. Learning agreement must be completed prior to registration (restricted).

Department: Math/Comp Sci/Statistics

**M 305 Discrete Structures I. 4 Credits**

Prerequisite(s): M 172 and CSCI 111A. (F) Covers logic, recursion, induction and basic data models.

Surveys combinatorics and the theory of algorithms with attention to design analysis and verification techniques.

Lecture Hours 4

Department: Math/Comp Sci/Statistics

**M 306 Discrete Structures II. 4 Credits**

Term Typically Offered: Spring

Prerequisite(s): M 305.

Discusses algorithm design in the context of graph theory. Introduces automata and formal languages. Covers logic, computability, artificial intelligence and robotics.

Department: Math/Comp Sci/Statistics

**M 329 Modern Geometry. 3 Credits**

Term Typically Offered: Spring

Prerequisite(s): M 333 or consent of instructor.

Deals with the fundamentals of synthetic and modern geometry. Covers topics in non-Euclidean geometry as well as topics in Euclidean geometry, such as finite geometry, space geometry, constructions, and solid geometry.

Lecture Hours 3

Department: Math/Comp Sci/Statistics

**M 330 History of Mathematics. 3 Credits**

Term Typically Offered: Fall

Emphasizes the historical development of mathematics during 5,000 years, from primitive counting through set theory. Particularly useful for those teaching mathematics.

Lecture Hours 3

Department: Math/Comp Sci/Statistics

**M 333 Linear Algebra. 4 Credits**

Term Typically Offered: Spring

Prerequisite: M 172. Covers linear systems and matrices, determinants, vector spaces, linear transformations, eigenvalues and eigenvectors, and orthogonality. Exact topics may vary year to year.

Lecture Hours 4

Department: Math/Comp Sci/Statistics

**M 371 Numerical Computing. 4 Credits**

Term Typically Offered: Spring

Prerequisite(s): M 333.

Presents floating-point arithmetic, approximate solution of equations and systems of equations, polynomial interpolation, numerical integration and differentiation, and the approximate solution of ordinary differential equations. Exact topics may vary from year to year.

Lecture Hours 4

Department: Math/Comp Sci/Statistics

**M 372 Scientific Computing. 3 Credits**

Department: Math/Comp Sci/Statistics

**M 397 Educ Methods: Peer Tutoring. 1 Credit**

Prerequisite(s): mathematics major or minor and approval of the director of the Math Lab.

R-3 Provides practical experience imparting basic mathematical skills to the students in the Math Lab.

Department: Math/Comp Sci/Statistics

**M 431 Abstract Algebra I. 3 Credits**

Term Typically Offered: Fall

Prerequisite: M 242 and M 333. Covers groups, rings, fields and vector spaces. Exact topics may vary from year to year.

Lecture Hours 3

Department: Math/Comp Sci/Statistics

**M 471 Mathematical Analysis. 3 Credits**

Prerequisite(s): M 242 and M 273.

Presents the basic theorems of one and multivariable analysis as a basis for higher analysis and its applications.

Lecture Hours 3

Department: Math/Comp Sci/Statistics

**M 472 Intro to Complex Analysis. 3 Credits**

Prerequisite(s): M 273.

Covers topics in multivariable calculus and/or complex variables.

Lecture Hours 3

Department: Math/Comp Sci/Statistics

**M 492 Independent Study. 1-4 Credits**

Prerequisites: consent of instructor and department chairperson. Provides outstanding students an individual opportunity to explore material not covered by regular mathematics courses.

Department: Math/Comp Sci/Statistics

**M 494 Seminar/Workshop. 1-4 Credits**

Prerequisite(s): mathematics major or minor, or consent of instructor.

Investigates intensively topics pertinent to the area of Mathematics.

Department: Math/Comp Sci/Statistics

**M 498 Internship/Cooperative Educ. 1-9 Credits**

Provides university credit for a work experience in the area of Mathematics, supervised by faculty. Learning agreement must be completed prior to registration (restricted).

Department: Math/Comp Sci/Statistics

**M 499 Capstone. 3 Credits**

Term Typically Offered: Fall

Prerequisite(s): Senior Standing in Math.

Requires students to analyze and create mathematical arguments that lead to written or oral reports. Synthesizes the ideas and techniques acquired in prior mathematics courses. Incorporates the department assessment exams.

Department: Math/Comp Sci/Statistics

**M 570 Independent Study. 1-3 Credits**

Term Typically Offered: Fall, Spring, Summer

Prerequisite(s): Graduate standing and permission of instructor.

Provides students an opportunity to explore material not covered by regular mathematics courses.

Department: Math/Comp Sci/Statistics

**M 580 Special Topics. 1-4 Credits**

Term Typically Offered: Fall, Spring, Summer

Prerequisite(s): Graduate standing and permission of instructor.

Investigates intensively topics pertinent to the area of Mathematics.

Lecture Hours 1-4

Department: Math/Comp Sci/Statistics

## Statistics

**STAT 141 Intro to Statistical Concepts. 3 Credits**

Term Typically Offered: Fall, Spring, Summer

Prerequisite(s): M 088 or equivalent.

Introduces the basic ideas of modern statistics including descriptive statistics, probability, and statistical inference.

Lecture Hours 3

Department: Math/Comp Sci/Statistics

**STAT 216 Introduction to Statistics. 4 Credits**

Term Typically Offered: Fall, Spring, Summer

Prerequisite(s): M 088 or equivalent.

Covers descriptive techniques, probability distributions, and statistical inference of one and two sample tests and associated confidence intervals for means and proportions and linear regression. Introduces statistical analysis using technology.

Lecture Hours 4

Department: Math/Comp Sci/Statistics

**STAT 217 Interm Statistical Concepts. 4 Credits**

Prerequisite(s): STAT 216 or consent of instructor.

Covers one and two sample tests and associated confidence intervals for means and proportions; one-way analysis of variance; F-tests; multiple comparisons; correlation; contingency tables; and distribution-free methods. Emphasizes statistical analysis using the computer.

Lecture Hours 4

Department: Math/Comp Sci/Statistics

**STAT 294 Seminar/Workshop. 1-8 Credits**

Department: Math/Comp Sci/Statistics

**STAT 341 Intro Probability & Statistics. 4 Credits**

Term Typically Offered: Fall

Prerequisite(s): M 273.

Covers discrete and continuous random variables, moment generating functions, statistical inference, and methods of estimation. Topics may vary from year to year.

Lecture Hours 4

Department: Math/Comp Sci/Statistics

**STAT 492 Independent Study. 1-3 Credits**

Prerequisites: consent of instructor and department chairperson. Provides outstanding students an individual opportunity to explore material not covered by regular statistics courses.

Department: Math/Comp Sci/Statistics

**STAT 494 Seminar/Workshop. 1-3 Credits**

Provides an opportunity for experimental study in an area of statistics.

Department: Math/Comp Sci/Statistics