Mathematics is one of the most intellectually challenging and academically pure subjects. Mathematical thought is a creative process of the mind that uses only logical deduction and established results which, in turn, have been derived from a few unarguable assumptions (axioms). Mathematical modeling is the process of critically investigating a given object (e.g., the functioning of a biological system); and of choosing or creating mathematical structures that explain the observed behavior and allow for prediction and manipulation of this object.

The mathematics program at Rocky Mountain College emphasizes both the pure and applied aspects of mathematics. At its core, its curriculum is designed to provide students with a solid foundation in the art of providing mathematically sound arguments, and with a thorough knowledge of the most important modern mathematical tools and methods. In addition, the mathematics program offers elective courses that give students the opportunity to branch out and pursue their own interests. Many elective courses emphasize connections to other fields (such as computer science, engineering, finance, and the natural sciences).

All mathematics prerequisite courses must be completed with a grade of at least “C”.

Major in Mathematics

A minimum of 38 semester hours, including:
MAT175 Calculus I
MAT176 Calculus II
MAT212 How to Read and Write Proofs
MAT275 Calculus III
MAT276 Introduction to Mathematica
MAT311 Linear Algebra
MAT313 Differential Equations
MAT317 Abstract Algebra I
MAT318 Abstract Algebra II
MAT481 Real Variables

Plus two electives numbered 219 or above.

Major in Mathematics Education

A minimum of 40 semester hours, including:
MAT175 Calculus I
MAT176 Calculus II
MAT212 How to Read and Write Proofs
MAT220 Elementary Number Theory
MAT256 Discrete Structures and Computability
MAT275 Calculus III
MAT276 Introduction to Mathematica
MAT306 History and Philosophy of Mathematics
MAT310 Mathematical Statistics
MAT312 Modern Geometric Theories
MAT317 Abstract Algebra I
MAT318 Abstract Algebra II
MAT422 Methods and Materials: Teaching Mathematics in the Secondary School
MAT481 Real Variables I

In addition, students must complete the professional education program for secondary teaching (grades 5-12) as described in the “education” section of the catalog.

Note: If a student majors in both mathematics and mathematics education, he or she must complete the requirements of both majors but does not need to take additional credits within the mathematics department. Majoring in both mathematics and mathematics education requires a minimum of 46 semester hours.

Minor in Mathematics

A minimum of 21 semester hours, including:
MAT175 Calculus I
MAT176 Calculus II
MAT275 Calculus III

Choose three of the following:
MAT212 How to Read and Write Proofs
MAT256 Discrete Structures and Computability
MAT310 Mathematical Statistics
MAT311 Linear Algebra
MAT313 Differential Equations
MAT317 Abstract Algebra
MAT320 Numerical Methods
MAT481 Real Variables

Minor in Mathematics Education

A minimum of 29 semester hours, including:
MAT175 Calculus I
MAT176 Calculus II
MAT210 Probability and Statistics
MAT212 How to Read and Write Proofs
MAT220 Elementary Number Theory
MAT306 History and Philosophy of Mathematics
MAT312 Modern Geometric Theories
MAT317 Abstract Algebra I
MAT422 Methods and Materials: Teaching Mathematics in the Secondary School

In addition, students must complete the professional education program for secondary teaching (grades 5-12) as described in the "education" section of the catalog.

MAT090 - Refresher Math: Algebra

Semester: Fall and Spring
Semester hours: 3
Sponsored by services for academic success (SAS), this course is designed to prepare students for college algebra. Elementary algebra topics are covered, which include solving equations and inequalities, simplifying algebraic expressions, simplifying expressions involving integers and rational numbers, and graphing equations. This course will not satisfy the math general education requirements and will not count toward the 124 credits required for graduation.

MAT100 - College Algebra

Semester: Fall and Spring
Semester hours: 3
This is a basic course in intermediate and advanced algebra.
Prerequisite: satisfactory score on a placement exam

MAT103 - Mathematics for Elementary School Teachers I

Semester: Fall
Semester hours: 3
A survey of various mathematical topics normally taught in grades K-8, specifically numeration systems, number theory, patterns and relationships, and fractions. This course is intended for elementary education students only. Students must earn a grade of "C-" or better to fulfill requirements for the elementary education program.
Prerequisite: MAT100 or satisfactory score on a placement exam

MAT104 - Mathematics for Elementary School Teachers II

Semester: Spring
Semester hours: 3
A survey of various mathematical topics normally taught in grades K-8, specifically probability and statistics, geometric basic concepts and structures, measurement, and coordinate geometry. This course is intended for elementary education students only. Students must earn a grade of "C-" or better to fulfill requirements for the elementary education program.
Prerequisite: MAT103 or satisfactory score on a placement exam

MAT110 - Elementary Functions

Semester: Fall and Spring
Semester hours: 3
A standard pre-calculus course emphasizing the function concept. Special attention is paid to trigonometric, exponential, and logarithmic functions.
Prerequisite: MAT100 or satisfactory score on a placement exam

MAT131 - Trigonometry and Applied Calculus

Semester: Fall
Semester hours: 3
This course is available to aeronautical science majors and aviation management majors only. This course introduces applied trigonometry, vectors, and basic differential and integral calculus to model and solve real-world problems.
Prerequisite: MAT100 or satisfactory score on a placement exam

MAT152 - To Infinity and Beyond

Semester: On Demand
Semester hours: 3
Exploration of a variety of modern mathematical topics. Topics will illustrate mathematics as a way of representing and understanding patterns and structures, as an art, as a tool in other disciplines and as a historical force. Topics may include infinity, chaos, fractals, symmetry, networks and others.
Prerequisite: MAT100 or the equivalent

MAT175 - Calculus I

Semester: Fall
Semester hours: 5
This course is a study of the functions of one real variable and includes a brief review of circular functions. The ideas of limit, continuity, and differentiation are explained and applied to physical problems. Topics include the use of approximations and problem solving. The use of graphing calculators is required.
Prerequisite: satisfactory score on a placement exam or MAT110

MAT176 - Calculus II

Semester: Spring
Semester hours: 5
Continuing the study of the functions of one real variable, the idea of integration is applied to physical problems. Introduction to sequences and series. The use of graphing calculators is required.
Prerequisite: MAT175

MAT210 - Probability and Statistics

Semester: Fall, Spring, and Summer
Semester hours: 3
This course provides a non-calculus-based study of discrete probability theory and its statistical applications. Distribution theory and its applications in hypothesis testing and setting confidence intervals are discussed.
Prerequisite: MAT100 or satisfactory score on a placement exam

MAT212 - How to Read and Write Proofs

Semester: Spring; Alternate Years
Semester hours: 3
Students are introduced to the different methods of mathematical proofs. Emphasis is placed on critical reading of proofs and the ability to correct errors as well as on writing correct proofs. This course is designed as a precursor to advanced math courses and should be taken during the freshman or sophomore year.
Prerequisite: MAT175

MAT219 - Graph Theory

Semester: On Demand
Semester hours: 3
Topics include paths, Euler and Hamiltonian problems, planar graphs, trees, directed and undirected graphs, networks, and connectedness. Applications to various disciplines will be included. Computational algorithms will be developed as appropriate.
Prerequisite: MAT100 or satisfactory score on a placement exam

MAT220 - Elementary Number Theory

Semester: Fall; Alternate Years
Semester hours: 3
Topics include axiomatic development of the positive integers, construction of the real number system, and study of equations with integral solutions. Divisibility properties, prime numbers, and the analysis of congruencies will be studied.
Prerequisite: MAT175 and MAT212

MAT256 - Discrete Structures and Computability

Semester: On Demand
Semester hours: 3
The mathematical and theoretical underpinnings of the science of computer science will be explored. Students will be introduced to Boolean algebra and elementary logic and their application to computer implementation and algorithm development. This course explores the historical development of computer science from its roots in mathematical models including early models of computation, such as Turing machines and other finite state machines.
Prerequisite: CSC131 or CSC143 and either MAT110 or MAT175

MAT275 - Calculus III

Semester: Fall
Semester hours: 3
Vector functions of one or more real variables, scalar functions of several variables, multiple integration, and surface theory via vectors are among the topics studied. Increasing emphasis on modeling of physical problems and the analysis of geometrical problems in higher dimensional space.
Prerequisite: MAT176

MAT276 - Introduction to Mathematica

Semester: Fall
Semester hours: 1
This course provides an introduction to the basic structures and components of computer algebra systems (CAS). Lists, functions, graphics and programming in Mathematica will be covered. Students are required to purchase a student copy of the software and install it on a personal computer.
Prerequisite: MAT176
Corequisite: MAT275

MAT306 - History and Philosophy of Mathematics

Semester: Fall; Alternate Years
Semester hours: 3
This course provides a survey of mathematicians of historical note, including their motivations and studies. Students will also examine classical problems and how they were solved. Unsolved problems in mathematics will be discussed.
Prerequisite: MAT175

MAT310 - Mathematical Statistics

Semester: Spring; Alternate Years
Semester hours: 3
A calculus-based introduction to statistical methods and theory. The course covers basic probability rules; random variables and probability distributions; limit theorems; sampling distributions; point and interval estimation methods; hypothesis testing, including t-and chi-square tests; the simple linear regression model and analysis of variance.
Prerequisite: MAT275

MAT311 - Linear Algebra

Semester: Spring; Alternate Years
Semester hours: 3
This course introduces students to the basic structures of linear algebra, which include the following: matrices, determinants, vectors and vector spaces, inner product spaces, eigenvalues and eigenvectors. Applications and computational aspects of these topics will be presented.
Prerequisite: MAT175
Corequisite: MAT176

MAT312 - Modern Geometric Theories

Semester: Spring; Alternate Years
Semester hours: 3
This course provides a study of Euclidean and non-Euclidean geometries.
Prerequisite: MAT175 and MAT212

MAT313 - Differential Equations

Semester: Fall; Alternate Years
Semester hours: 3
his course examines analytic, numerical, and geometric techniques for solving first-order differential equations; bifurcations of first-order autonomous differential equations; second-order differential equations, with emphasis on the harmonic oscillator; Laplace transforms; eigenvalue/eigenvector and geometric methods for linear systems with constant coefficients; equilibrium point analysis of nonlinear systems; analysis of limit cycles. Applications from biology, physics, and economics are presented.
Prerequisite: MAT311

MAT316 - Complex Variables

Semester: On Demand
Semester hours: 3
This is a basic undergraduate course in complex variables. Topics will include analytic functions, Cauchy's integral formula, the residue calculus, and conformal mapping.
Prerequisite: MAT275

MAT317 - Abstract Algebra I

Semester: Fall; Alternate Years
Semester hours: 3
This course provides an introduction to algebraic structures via group theory. Students explore a careful development of the concept of a group and elementary properties of groups. Emphasis is placed on creating mathematical proofs. Some applications to physical problems are included.
Prerequisite: MAT275 and MAT212

MAT318 - Abstract Algebra II

Semester: Spring; Alternate Years
Semester hours: 3
This course is an extension of Abstract Algebra I, with ring, ideal, and field theory introduced and examined. Some Galois theory may be covered.
Prerequisite: MAT317

MAT320 - Numerical Methods

Semester: On Demand
Semester hours: 3
The study of numerical methods involves the design and use of algorithms for solving large mathematical problems with a computer. Topics include estimation of accuracy, the use of series and approximation, and numerical integration and differentiation.
Prerequisite: CSC251 and MAT176

MAT325 - Combinatorics

Semester: On Demand
Semester hours: 3
This basic course in enumerative Combinatorics emphasizes developing combinatorical reasoning skills and applying these to solve problems in various areas of math and computer science. Topics covered will include basic counting principles, generating functions, recurrence relations, the
principle of inclusion/exclusion, estimation, and modeling.
Prerequisite: MAT219

MAT422 - Methods and Materials: Teaching Mathematics in the Secondary School

Semester: On Demand
Semester hours: 2
This course requires focused study and consultation with a public school mathematics teacher, or other acceptable professional. Hours will be arranged in consultation with the content area professor, the secondary education professor, the student, and the professional mentor. Methods of teaching mathematical content appropriate for grades 5-12 are explored. Appropriate use of technology and implications of current research in mathematics education are discussed. Current NCTM curriculum standards are used as the foundation of the course.
Prerequisite: admission to the teacher education program, senior standing

MAT450 - Internship

Semester: On Demand
Semester hours: 1-12
An internship in mathematics arranged between a member of the math faculty and the student. The internship will not count as part of the minimum number of credits required in the major. The requirements will be based on the number of credits. Contract is required.
Prerequisite: junior or senior standing, a cumulative GPA of at least 2.00 and a major GPA of at least 2.25

MAT481 - Real Variables I

Semester: Spring; Alternate years
Semester hours: 3
Standard introductory course in real variables. Topics include: axioms of real numbers, cardinality of sets, topology of the real number line, supremum and infimum, Bolzano-Weierstrass theorem, sequences of real numbers, convergence of sequences, Cauchy sequences, limit theorems, continuity and uniform continuity of functions.
Prerequisite: MAT275 and MAT212

MAT482 - Real Variables II

Semester: On Demand
Semester hours: 3
Further topics in real variables, including: Riemann integration, differentiation of functions, mean value theorem and the fundamental theorem of calculus, sequences of functions, pointwise and uniform convergence, limit theorems, special functions. Other topics if time permits may include the following: metric spaces, uniform norm, spaces of functions, series of real numbers, and others.
Prerequisite: MAT481

MAT490 - Seminar

Semester: On Demand
Semester hours: 2-3
Selected topics in mathematics are explored.
Prerequisite: permission of professor

MAT499 - Independent Study

Semester: On Demand
Semester hours: 1-3
This course allows interested students to devise and pursue independent study in an area agreed upon in consultation with, and supervised by, a faculty member. Students should be either a major or minor in mathematics or mathematics education and have a cumulative GPA of 3.00 or greater.
Prerequisite: junior or senior standing