Mathematics
The Department of Mathematics awards both the Bachelor of Arts and Bachelor of Science in Mathematics. The undergraduate major programs meet the needs of students who: (a) are preparing to teach mathematics at the secondary or two-year college level; (b) plan a career in business or industry using mathematics; or (c) plan to continue to study mathematics at the graduate level. Depending on their career goals, students choose one of two emphases: teaching or industrial/academic. Courses for students who want some knowledge of mathematics as part of a liberal education, or who are preparing to teach at the elementary school level, are also available.
Department of Mathematics Faculty Listing
Academic Programs
Mathematics - BA Mathematics - BS Mathematics MinorCourses
An independent study course in which the student individually or as a member of a team assigns, creates, and implements a total package for a particular machine or system. May be repeated once with the permission of the instructor.
This course is designed to serve as preparation for MATH 110. Topics include properties of real numbers, linear and quadratic equations, absolute value equations and inequalities, systems of linear equations and inequalities, operations on polynomials and factoring, operations on rational equations, graphs of functions, integer and rational exponents, and radicals. Students completing this course will have 2 or 3 credit hours added to the minimum degree requirements.
This course offers a survey of various mathematical topics for the non-math/science major. In addition to skill development, mathematics will be studied with an emphasis on real-world application spanning many disciplines to support the concept that math impacts much of our everyday lives.Topics may include algebra, geometry, probability and statistics, the real number system, and logic.
A study of equations, graphs, and inequalities for linear, quadratic, polynomial, rational, logarithmic, exponential, and absolute value functions. Transformations on graphs, complex numbers, circles, systems of inequalities, and systems of equations including matrices.
A study of equations, graphs, and inequalities for linear, quadratic, polynomial, rational, logarithmic, exponential, and absolute value functions. Thansformations on graphs, complex numbers, circles, systems of inequalities, and systems of equations including matrices.
In-depth study of trigonometry including definitions, unit circle and right triangle properties, identities, functions and their inverse, solving equations, graphing, solving triangles, and application to real world. Additional topics of polar coordinates and complex numbers may also be included.
In-depth study of linear, quadratic, absolute value, and rational equations and inequalities; polynomial, rational, exponential, and logarithmic functions; complex numbers; linear and non-linear systems of equations and inequalities; unit circle and right triangle trigonometry; law of sines and cosines; graphs of trigonometric functions; and verifying trigonometric identities.
For the prospective teacher of elementary school mathematics. Detailed study of place value, arithmetic operations, exponentiation, mental math, fractions, factorization, integers, ratios, and percent in the context of the real number system.
This course is designed to receive non-equivalent elective transfer credit.
Composition of, and resolution of forces; equilibrium of force systems; application of general laws of statics, including use of vector algebra, friction and force analysis of simple structures; centroids; moments of inertia.
A study of algebraic and transcendental functions of one variable in the areas of analytic geometry, limits, continuity, derivatives, and integrals. This study includes computations of derivatives throughbasic derivative rules (sum, product, quotient, chain, etc.), implicit differentiation, differentiation ofparametric equations, applications of derivatives (optimization and related rate), mean-value theorem, definite integral, the fundamental theorem of calculus, introductory integration techniques including substitution and parts, approximation of integrals, improper integrals, and introductory applications of definite integrals (area, volume, total accumulation).
A continued study of algebraic and transcendental functions of one variable in the areas of analytic geometry in two dimensional Cartesian and polar systems, analytic geometry in three dimensional Cartesian systems, advanced integration techniques, sequences, series, differential equations, and vectors. This study includes computations of derivatives and integrals in polar coordinates, analysis of the hyperbolic trig functions, integration by change of variable, further applications of integration (to arc length, physics, engineering, economics, biology, statistics), modeling with differential equations (especially exponential growth and decay), approximate solutions to differential equations, solutions of seperable differential equations, convergence and divergence of sequences and series, representations of functions as Taylor/ power series, vector representations, vector arithmetic including dot and cross products.
A study of functions of several variables in the areas of analytic geometry in primarily three dimensional coordinate systems (Cartesian, cylindrical, spherical) including vector properties, vector representation of functions and surfaces, the calculus of functions of several variables, and the calculus of vectors. This study includes vector dot and cross product applications, vector and non-vector representation of curves and surfaces in three dimensions, derivatives and integrals of vector functions, applications of vector functions in arc length/ curvature/velocity/acceleration, limits and continuity in functions of several variables, partial derivatives, tangent planes, chain rule, directional derivatives, gradients, optimizations, Lagrange multipliers, multiple integrals, applications of multiple integrals including surface area/volume/center of mass, change of variables in multiple integration, line integrals, curl, divergence, Green's Theorem, surface integrals, Stoke's Theorem, and the Divergence Theorem.
Basic concepts and applications (conic sections, systems of differential equations) of linear algebra and matrix theory including vector algebra in two, three and n-dimensional space, Eigen Values, Eigen Vectors, QR decomposition, diagonalization, Orthogonality, Gram-Schmidt Process, Linear Transformations, Linear dependence, Linear Independence, Norms, Vector Space, Subspace, Kernel, Range, and Inner Product Space.
A study of sampling methods, distributions, measures of central tendency and dispersion, probability, binomial and normal distributions, Central Limit Theorem, confidence intervals, hypothesis testing for means and proportion, correlation, and regression.
Provides prospective middle and high school teachers with 20 hours of classroom observation and written reflection of various topics related to mathematics instruction.
A first course for the prospective middle or high school math teacher. Discussion of methodology for preparation and presentation of mathematical content, presentation of lessons, and review and mastery of 7-12 math content.
An enrichment course in which selected topics, not covered in standard courses, will be explored.
The course will focus on mathematical logic and the main proof techniques used in writing mathematical arguments. This will involve reading proofs to gain deep understanding, studying common mathematical logic statements and proof techniques, and developing and communicating rigorous mathematical proofs. Proofs techniques will include, but not be limited to, direct (deductive) proof; proof by exhaustion; indirect proof (by contradiction, or by contrapositive); mathematical induction; disproof by counterexample.
A mathematical content (not methods) course for the prospective teacher of elementary school mathematics. Detailed study of the content and conceptual development of measurement, transformational geometry, two and three dimensional figures, symmetries, congruence and similarity.
Non-math majors only. Techniques from calculus including limits, derivatives, and integration applied to business and sciences.
A study of probability, discrete and continuous distributions, expected value and dispersion, moment generating functions, joint distributions, correlation and regression, estimation, and hypothesis testing.
First order differential equations, linear equations with constant coefficients, and some special higher order equations, with applications which may include Laplace Transforms, Systems of Linear Differential Equations, Stability of Dynamical Systems, and Caley-Hamilton Theorem.
A study of the historical development of modern mathematical ideas and the contributions of major mathematicians and cultures from ancient times through Calculus.
Discussion of methods of teaching, collection and creation of mathematics teaching materials, preparation of a unity of study and performacne assessment, and presentation of lessons.
This course is designed to receive non-equivalent elective transfer credit.
A first study of abstracted algebraic structures including investigation of groups, rings, integral domains, and fields. This study investigates, conjectures, and proves key properties on various concrete and abstracted sets of objects (sets of numbers, permultations, polynomials, matrices, symmetries, etc.) including the division algorithm in the integers, Euclid's Algorithm, unique factorization in the integers, permutations of finite sets, abstracted group properties, subgroup properties, cyclic groups, modular arithmetic, normal subgroups, cosets of subgroups, quotient groups, mappings, group isomorphisms, group homomorphisms, Cayley's Theorem, abstracted ring properties, subring properties, ring homomorphisms, ideals, abstracted integral domain properties, abstracted field properties, and applications to specific sets.
A first study of abstracted algebraic structures including investigation of groups, rings, integral domains, and fields. This study investigates, conjectures, and proves key properties on various concrete and abstracted sets of objects (sets of numbers, permultations, polynomials, matrices, symmetries, etc.) including the division algorithm in the integers, Euclid's Algorithm, unique factorization in the integers, permutations of finite sets, abstracted group properties, subgroup properties, cyclic groups, modular arithmetic, normal subgroups, cosets of subgroups, quotient groups, mappings, group isomorphisms, group homomorphisms, Cayley's Theorem, abstracted ring properties, subring properties, ring homomorphisms, ideals, abstracted integral domain properties, abstracted field properties, and applications to specific sets.
A review of Euclidean constructions and a study of geometric topics developed during the last few hundred years. Topics include finite geometries, transformation groups, transformations in two and three dimensions, circle inversion, Taxicab Geometry, and projections.
A review of Euclidean constructions and a study of geometric topics developed during the last few hundred years. Topics include finite geometries, transformation groups, transformations in two and three dimensions, circle inversion, Taxicab Geometry, and projections.
Functions of a single real variable: Completeness Axioms, sequences, continuity, differentiation, functions as solutions of Differential Equations, Fundamental Theorems of Integrations, Riemann integration, and Taylor Polynomials.
Functions of a single real variable: Completeness Axioms, sequences, continuity, differentiation, functions as solutions of Differential Equations, Fundamental Theorems of Integrations, Riemann integration, and Taylor Polynomials.
Functions of several real variables: linear transformations, continuity, and differentiabilty, Inverse/Implicit Function Theorems, multiple integrals, and line and surface integrals.
Functions of several real variables: linear transformations, continuity, and differentiabilty, Inverse/Implicit Function Theorems, multiple integrals, and line and surface integrals. D
An elementary working knowledge of the application of vectory analysis, differential equations, orthogonal functions, complex variables, probability and statistics.
An elementary working knowledge of the application of vectory analysis, differential equations, orthogonal functions, complex variables, probability and statistics.
An introduction to mathematical models. Topics include Markov chains, linear programming, game theory, and networks and flows.
An introduction to mathematical models. Topics include Markov chains, linear programming, game theory, and networks and flows. I
Discrete mathematical structures with applications in computer science/software engineering. Topics include trees, graphs, and combinatorics.
Discrete mathematical structures with applications in computer science/software engineering. Topics include trees, graphs, and combinatorics.
In-depth study of proabability concepts and their application in statistics. Topics include random vairables, joint distributions, generating functions, sampling distributions, confidence intervals, hypothesis tests, least-squares, correlation.
In-depth study of proabability concepts and their application in statistics. Topics include random vairables, joint distributions, generating functions, sampling distributions, confidence intervals, hypothesis tests, least-squares, correlation.
Partial differentiation, solution of partial differential equations including the use of Fourier series with applications to physics.
Partial differentiation, solution of partial differential equations including the use of Fourier series with applications to physics.
Applications of mathematics to selected problems from the natural sciences.
Applications of mathematics to selected problems from the natural sciences.
The algebra and geometry of vectors, the calculus of vectors with applications. An introduction to tensors as time permits. D
The algebra and geometry of vectors, the calculus of vectors with applications. An introduction to tensors as time permits.
Numerical differentiation and integrations, Richardson interpolations, different quadratures, numerical techniques for solving non-linear equations, systems of linear equations, and ordinary differential equations. Fixed-point iteration, interpolation, Romberg integration and predictor-corrector methods. Numerical solutions of heat, wave, and potential equations.
Numerical differentiation and integrations, Richardson interpolations, different quadratures, numerical techniques for solving non-linear equations, systems of linear equations, and ordinary differential equations. Fixed-point iteration, interpolation, Romberg integration and predictor-corrector methods. Numerical solutions of heat, wave, and potential equations.
Basic set theory and cardinal and ordinal numbers and their arithmetic. Basic concepts of topology in the context of metric spaces.
Basic set theory and cardinal and ordinal numbers and their arithmetic. Basic concepts of topology in the context of metric spaces.
A study of integers including theorems on divisibility, primes, theory of congruence, and Diophantine equations and applications to cryptography.
A study of integers including theorems on divisibility, primes, theory of congruence, and Diophantine equations and applications to cryptography.
Problems from or an investigation of some phase of mathematics possibly not treated in a regular course.
Problems from or an investigation of some phase of mathematics possibly not treated in a regular course.
Students prepare a paper on a mathematics or mathematics education topic and give an oral presentation to Mathematics and Computer Science faculty and students.
Students prepare a paper on a mathematics or mathematics education topic and give an oral presentation to Mathematics and Computer Science faculty and students.
Content varies, but may be a study of supplementary topics to be used as enrichment in the teaching of mathematics in the elementary and secondary school.
Content varies, but may be a study of supplementary topics to be used as enrichment in the teaching of mathematics in the elementary and secondary school.
Basic set theory and cardinal and ordinal numbers and their arithmetic. Basic concepts of topology in the context of metric spaces. Recommended for teachers. D
A study of theorems about integers. Topics include theorems on divisibility, theory of congruences, diophantine equations and quadratic reciprocity. Recommended for teachers. I
Miscellaneous problems from or an investigation of some phase of undergraduate mathematics possibly not treated in a regular course.
Emphasis on problem-solving strategies and historical development of various areas of mathematics. Designed for mathematics teachers.
A study in the theory of algebraic structures including group, ring, integral domain, and field theory. This study investigates the theory of groups, subgroups, normal subgroups, quotient groups, permutation groups, Sylow theorems, direct products, finite Abelian groups, rings (commutative and non commutative), integral domains, group/ ring homomorphisms, group/ring automorphisms, ring ideals, quotient rings, Euclidean rings, polynomial rings, fields.
A continued study of the theory of algebriac stuctures primarily of fields and linear spaces. This study investigates the theory of fields, solvability, extension fields, vector spaces over a field, dual spaces, inner product spaces, the elements of Galois Theory, applications of Galois Theory to roots of polynomials and construction with straightedge and compass.
Development of basic topological concepts such as continuity, metrizability, connectedness, compactness and various separation properties.
Study of algebraic and geomestric representation of complex numbers, differentiations and integrations, Cuachy-Riemann Equations, Cauchy's Integral Theorem, harmonic functions, power series, Taylor and Laurent Series, Singularities and Residue Theorem.
A study of the classical theory of functions of a real variable, measure and integration, point set topology and normed linear spaces.
The study of probability topics may include the law of large numbers, conditional expectations, characteristic functions, the central limit theorem, random walks, martingales, Markov Chains, and Brownian Motion.
Techniques of teaching mathematics for the teacher-in-service. Research based practices applied to learning strategies and curriculum design.
Directed readings and written reports/reflections on recent literature in mathematics education.
Students prepare a research paper on a mathematics or mathematics education topic and give an oral presentation to the Mathematics and Computer Science faculty and students.
Topics of current interest and value for practicing teachers.
Issues and trends in the teaching of geometry; content areas in geometry; dynamic software; and roles of axiomatics and problem solving in geometry.
Issues and trends in the teaching of algebra; balance between rigor and manipulation in algebra; content areas in algebra; enrichment and problem solving in algebra.
A study of algebra, geometry, and trigonometry through the lens of calculus. Issues and trends in the teaching of rates of change, sequences and series, limits, derivative and integrals.
Issues and trends in the teaching, use and role of problem solving in the teaching of mathematics.
Issues and trends in the teaching of probability and statistics through emphasis on applications and statistical thinking.
Content varies. Study of supplementary topics to be used as enrichment in the teaching of mathematics in the elementary, middle, and secondary school.
Fort Hays State University
600 Park Street
Hays, KS 67601-4099
785-628-FHSU (3478)