Mathematics
Introduction
Today, many professions require employees to possess quantitative and analytical skills. In truth, employers are seeking applicants who have more than factual knowledge; instead, they want applicants who possess good problem-solving skills, the ability to think and reason analytically, and the ability to continue to learn on the job. Because mathematics is rooted in logic and is a fundamental tool for many other fields, particularly those in the natural and social sciences, it is the ideal discipline to study in an effort to acquire these necessary skills and prepare for successful careers in an ever-changing society.
A degree in Mathematics can provide the foundation needed to launch a career in teaching, industry, government agencies, insurance companies, and many other fields. Majors may also go on to graduate programs in mathematics, statistics, actuarial science, law, and other areas.
In particular, recent LC Mathematics graduates have secured positions
- teaching mathematics at various levels;
- working for the U.S. Census Bureau; and
- in mathematical-related industries, including supervisory positions in these industries.
LaGrange College Mathematics graduates have also successfully completed graduate programs in
- mathematics
- mathematics education
- statistics
- law school
Mission Statement
The Mathematics Program supports the College’s commitment to the liberal arts education of its students by using mathematics as a means to improve students’ critical thinking, communicative, and creative abilities, through the exploration of abstract and applied mathematics, in a caring and supportive environment.
Program Objectives
The Mathematics Program strives to provide
- opportunities for all students to increase their understanding of mathematics as a discipline, measured by individual course assessments in all Core Mathematics classes (Core Understanding of Mathematics); and
- a well-rounded curriculum that prepares the Mathematics majors for graduate study in mathematic-related fields or employment in a variety of related fields, measured by data on graduates and alumni survey (Future Endeavors).
Learning Outcomes
- Students in Core classes will demonstrate the abilities to think critically and creatively and to communicate mathematics effectively.
- Students completing a B.A. or B.S. in Mathematics should be able to
- demonstrate an understanding of key mathematical concepts in the following areas:
- Algebra and Number Theory
- Measurement, Geometry, and Trigonometry
- Functions and Calculus
- Data Analysis, Statistics, and Probability
- Matrix Algebra and Discrete Mathematics
- present a creative/original solution to a mathematics question that is new to the student and that:
- demonstrates effective communication skills,
- uses appropriate notation and terminology, and
- includes a valid and logical mathematical argument.
- demonstrate an understanding of key mathematical concepts in the following areas:
- Students completing a B.S. in Mathematics with a concentration in Computational Mathematics should be able to
- demonstrate the ability to program simple numerical algorithms in MATLAB or other programming environments.
- obtain and utilize useful information from unrefined data, using mathematical and statistical techniques.
- make appropriate assumptions to create a mathematical model that accurately represents a physical phenomenon, one that is amenable to solutions with a
Assessment of Learning Outcomes
- At least 75% of students in Core Mathematics courses will demonstrate improvement on post-course exams (from pre-course exam scores).
- a) At least 60% of graduating Mathematics majors will earn a score of 58% or higher on the Mathematics: Content Knowledge Praxis exam (Test Code: 0061 of the Praxis Series). A score of 58% is the largest minimum score required by any state that administers the Praxis exam as part of the secondary teacher certification process. b) The accomplishment of this outcome will be demonstrated by the satisfactory performance of the student in delivering the presentation at a mathematics conference seminar during the final semester of the student’s senior year. The topic of this presentation will be assigned by the Mathematics faculty no later than the end of the student’s penultimate semester at LaGrange College. At least four (4) faculty members will be present and will rate the student on a five-point scale for each of I – III above. A satisfactory score will be achieved if the student receives an average score of 3 or higher in each area.
- A comprehensive exam that focuses on the three (3) Learning Outcomes will be administered at the end of each student’s final Mathematics course associated with the Computational Mathematics concentration (either MATH 3092 or MATH 3185). This exam will be graded independently by at least two (2) members of the Mathematics faculty. At least 70% of the students completing the Computational Mathematics concentration will earn a score of 65% or higher on this exam.
In addition, a survey is sent to recent graduates of the program during the Fall term of each year. The results of these surveys are considered and may result in changes to improve the program.
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Majors and Minors
Major Minor
B.S. in Mathematics B.A. in Mathematics Minor in Mathematics B.S. in Mathematics with a Concentration in Computational Mathematics Minor in Computational MathematicsCourses
An introduction to algebra. Topics include instruction in real numbers, graphs, algebraic expressions, equations, and polynomials.
A study of sets, real numbers, operations, order, inequalities, polynomial factoring, functions, graphs, exponents, first- and second-degree equations, and systems of equations.
An introduction to probability and statistics. Topics include descriptive statistics, probability, normal probability, confidence intervals, hypothesis testing, and linear regression. Offered in Fall and Spring terms.
Individual and small-group problem solving geared toward real-life situations and nontraditional problems. The course focuses on a number of problem-solving strategies, such as drawing a diagram, eliminating possibilities, making a systematic list, looking for a pattern, guessing and checking, solving an easier related problem and sub-problems, using manipulatives, working backward, acting it out, unit analysis, using algebra and finite differences, and others. Divergent thinking and technical communication skills of writing and oral presentation are emphasized.
A study of calculus-oriented algebra and trigonometry. Topics include simplifying algebraic expressions, solving equations, exponential and logarithmic functions, applications of functions, graphs, and the trigonometric functions.
An introduction to differentiation and integral calculus. Topics include limits, differentiation and applications, integration, and the calculus of exponential and logarithmic functions. Prerequisite: A grade of C- or better in MATH 2105 or 1121 (and permission of instructor) or satisfactory Mathematics placement recommendation.
A continuation of MATH 2221. Topics include the applications of integration, the calculus of inverse trigonometric functions, techniques of integration, indeterminate forms, improper integrals, sequence and series, and the parametric equations, and the polar coordinates. Prerequisite: A grade of C- or better in MATH 2221 or appropriate AP credit for MATH .
A continuation of MATH 2222. Topics include vectors and vector-valued functions of several variables, multiple integration, and vector analysis. Prerequisite: A grade of C- or better in MATH 2222 or appropriate AP credit for MATH 2221 and MATH 2222.
An introduction to differential equations. Topics include the study of first and second-order differential equations, first-order systems, linear systems, Laplace transforms, and numerical methods.
A first course in mathematical programming in MATLAB that ranges from basic programming to the implementation of higher-level mathematics. Additional topics include learning a typesetting system (LaTeX) for producing technical and scientific documentation.
A study of the storage of data and the procedures used to extract and organize valuable information.
A thorough introduction to mathematical modeling techniques. Topics include the quantification of physical processes, model predictions and natural systems, and model comparisons and results.
Topics include Fourier Series, the Wave Equation, the Heat Equation, Laplace's Equation, Dirichlet Problems, Sturm-Liouville Theory, the Fourier Transform, and Finite Difference Numerical Methods. Offered on demand.
A study of the concepts of plane Euclidean geometry, with an introduction to coordinate geometry and non-Euclidean geometries. Offered on demand.
An Introduction to probability theory. Topics include random variables, method of enumeration, conditional probability, Baye’s theorem, discrete distributions (binomial distribution, and Poisson distribution), continuous distributions (uniform distribution, exponential distribution, gamma distribution, chi-square distribution, and normal distributions), Multivariate distributions. Offered in Spring semesters of even years.
An introduction to the mathematical theory of statistics. Topics include estimation and maximum likelihood estimates, sampling distributions, confidence intervals, and hypothesis testing.
An introduction to linear algebra and matrix theory. Topics include vectors, systems of linear equations, matrices, eigenvalues, eigenvectors, and orthogonality. Offered in spring terms.
An historical development of mathematical concepts.
An introduction to discrete mathematics. Topics include set theory, combinatorics, recurrence relations, linear programming, and graph theory.
An introduction to complex variables. Topics include complex numbers, analytic functions, elementary functions, complex integration, series representations for analytic functions, residue theory, and conformal mapping. Offered in Spring terms of odd years.
A study of techniques used for constructing combinatorial designs. Basic designs include triple systems, Latin squares, and affine and projective planes.
An introduction to modern abstract algebra.
A continuation of Modern Algebra I.
An introduction to Analysis.
A continuation of Analysis I.
A study of problem-solving techniques selected from the spectrum of Mathematics coursework required to complete a Mathematics major at LaGrange College. Topics come from a variety of areas, including algebra, trigonometry, geometry, calculus, discrete mathematics, probability and statistics, and mathematical reasoning and modeling. Offered in Spring terms.
An introduction to numerical analysis with computer solutions. Topics include Taylor series, finite difference, calculus, roots of equations, solutions of linear systems of equations, and least- squares. Offered on demand.
A second course in numerical analysis with computational solutions. Topics include solutions to ordinary and partial differential equations, higher-order quadratures, curve-fitting, and parameter estimation.
Internship.
This course allows students to pursue a special problem or topic beyond those encountered in any formal course. Course may be offered for variable credit.
This course allows students to pursue a second special problem or topic beyond those encountered in any formal course. This course may be taken for variable credit.
Special topics in Mathematics.