Mathematics at Bluffton College


One goal of the Mathematics Department is to prepare Mathematics majors for a wide variety of vocations and professional positions that value analytical reasoning skills, mathematical knowledge and problem-solving skills. The Mathematics Department embraces the Bluffton College institutional goal of emphasizing individual inquiry, critical thinking and lifelong learning.

The Mathematics Department maintains a program for Mathematics majors which guarantees both depth and breadth. Each student is required to study several areas of mathematics to a depth reasonable for an undergraduate. Our program endeavors to prepare students for positions in business, industry, actuarial mathematics, teaching and graduate school. We anticipate that some of our graduates will find careers in other professional positions as diverse as law, music and the pastorate.

A related goal of the Mathematics Department is to provide service to other departments by offering courses in mathematics appropriate for students in business, social sciences, physical and life sciences and elementary education.

Major (43 hours minimum)
Bluffton College placement tests and advanced placement tests taken in high school will be considered to assist appropriate placement and potential credit or waivers. The following courses are required:

MAT 135 Calculus 1 (5)
MAT 136 Calculus 2 (5)
MAT 220 Discrete Mathematics (3)
MAT 225 Multivariate Calculus (3)
MAT 230 Linear Algebra (3)
MAT 211 Introductory Geometry (3)
MAT 312 Advanced Geometry (alternate year) (3)
MAT 332 Abstract Algebra 1 (alternate year) (3)
MAT 340 Probability and Statistics (3)
MAT 350 Differential Equations and Modeling (alternate year) (3)
MAT 360 Operations Research (alternate year) (3)
MAT 401 Analysis (alternate year) (3)
CPS 108 Computer Programming (3)

CPS 320 and PHY 211 are strongly recommended for all Mathematics majors.

Restrictions and alternatives
At least one of the required upper level courses shall be taken during the senior year. Departmental honors may be sought by a student majoring in Mathematics by way of an approved plan of independent studies. MAT 390 may be considered as an elective in mathematics and is repeatable as distinct investigations.

Certification to teach mathematics
To become certified to teach mathematics as the primary field in secondary schools, a student must fulfill requirements for the Mathematics major and the professional education requirements at Bluffton College. Elementary teachers may choose mathematics as the area of concentration.


Minor (19 hours)
Required:

MAT 135 Calculus 1 (5)
MAT 136 Calculus 2 (5)

These courses (10 semester hours) comprise the complete first year calculus including infinite series.

Electives:
Select at least three of the following mathematics courses, of which at least one shall be numbered above 300 for a total minimum of 30 quarter hours.

MAT 220 Discrete Mathematics (3)
MAT 225 Multivariate Calculus (3)
MAT 230 Linear Algebra (3)
MAT 340 Probability and Statistics (3)
MAT 350 Differential Equations and Modeling (3)
MAT 360 Operations Research (3)
CPS 320 Numerical Analysis (3)

Substitutions of other courses will not be permitted for either the major or the minor in Mathematics except by approval of the Mathematics Department chair.


Courses
MAT 050 Basic Mathematics (3) (only 2 count toward graduation)
Students will review and apply basic computational and algebraic concepts and skills. Problem solving is a major focus of the course, including basic applications to geometry. Graphing calculators are provided and used throughout the course whenever appropriate.

MAT 100 College Algebra (3)
This course presents concepts and skills typically found in a college algebra course including development of real number systems, simplifying algebraic expressions, solving equations and inequalities and solving mathematical problems that model real world situations. Numerical, algebraic and graphical representations are used through out the course. Graphing calculators are required and are used to accommodate numerical and graphical solution techniques in addition to traditional paper and pencil methods. Prerequisites:
MAT 050 or two years of high school mathematics and qualification for placement.

MAT 105 Understanding Numerical Data (2)
Designed to help students understand, interpret and think critically about numerical information. The main focus of the course is concept development rather than mathematical manipulation. Use of graphing calculators will give students experience in handling numerical data. Prerequisites:
MAT 050 or placement into MAT 100 or above.

MAT 114 Pre-calculus (4)
A study of families of elementary functions and their important properties - power functions, polynomials, logarithmic and trionometric and inverse of each. Numerical, algebraic and graphical representations of each family are included. Polya’s problem-solving methods will be used to solve mathematical problems that model real world situations. Graphing calculators are required and are used extensively. Prerequisites: three years high school math and qualification for placement.

MAT 115 Business Calculus (3)
A study of functions and applied differential calculus for economics, business and other social sciences. Emphasis is on spreadsheet analysis of common elementary situations. Other topics covered include systems of linear equations and an introduction to linear programming.

MAT 135 Calculus 1 (5)
The fundamental concepts and applications of the differential calculus of one variable are applied to elementary families of functions. Polya’s problem-solving methods are used to solve mathematical problems that model real world situations and which require methods of differential calculus for their solution. Graphing calculators are required and are used extensively. Projects that require use of computer algebra systems such as Mathematica or Maple are included. Projects that require the historical roles of Newton and Leibnitz are included. Prerequisites:
MAT 114 or four years of high school math and qualification for placement.

MAT 136 Calculus 2 (5)
The fundamental concepts and applications of the definite integral of one variable, introductory differential equations, and infinite series, differential equations including series solutions. Problem-solving methods are applied to solve mathematical problems that model real world situations and which require methods of integral calculus for their solution. Graphing calculators are required and are used extensively. Projects that require historical roles of Newton and Leibnitz are included. Prerequisites:
MAT 135 or its equivalent.

MAT 185 Fundamental Mathematics Concepts for Early Childhood (3)
This course includes pre-number ideas, early number concepts, numeration systems, place value foundations and applications, understanding the basic algorithms of arithmetic, techniques of estimation, problem solving methods, basic concepts of geometry and measurement. Calculators and their role in mathematical problem solving are included from the perspective of learning to judge the most effective approach to a problem - estimation, mental calculation, paper and pencil or calculator. Prerequisite:
MAT 050 or readiness for college algebra (or higher) on mathematics placement.

MAT 186 Fundamental Mathematics Concepts for Middle Childhood (3)
This course includes the content of integers and fractions, rational and irrational numbers, decimal notation, ratio and percent, equations and inequalities, probability and motions in geometry. Calculators and their role in mathematical problem solving are included from the perspective of learning to judge the most effective approach to a problem - estimation, mental calculation, paper and pencil or calculator. Prerequisite:
MAT 185.

MAT 220 Discrete Mathematics (3)
This course introduces the student to general methods of discrete mathematics on topics selected from sets, relations and functions, graphs, trees, matching problems, counting techniques and recurrence. An algorithmic approach to problem solving will be a common thread that ties these various topics together. Historical contributions of mathematics to number theory and algebra are discussed, particularly those of Cantor, Euler, Fibonacci, Hamilton, Gauss, Boole and Russell. Prerequisite: qualification for placement at the calculus level.

MAT 211 Introductory Geometry (3)
A study of classical theorems from plane Euclidean geometry. Discovery methods and inductive reasoning are used with the computer program Cabri Geometry as a tool to discovery relationships. Four proof methods - vector, analytical, synthetic, and transformation - are compared and contrasted as discovered relationships are proven. The historical contributions of Greek, Indian, Arabs and European mathematicians are discussed, particularly those of Euclid, Pythagoras, Desargues, Pappus, Archimedes, Ptolemy, Heron, Brahmagupta, Bhaskara, Fermat, Poincare, Ceva, Minkowski, Steiner and Feuerbach. Prerequisite:
MAT 136.

MAT 225 Multivariate Calculus (3)
A development of vector calculus, partial derivatives and multiple integrals, properties of vectors and transformations on coordinate systems, line and surface integrals, projects that make use of systems such as Mathematica or Maple for three dimensional display are included throughout the course. Prerequisite:
MAT 136.

MAT 230 Linear Algebra (3)
A study of vector spaces and subspaces, linear transformations, matrices and determinants, eigenvalues and eigenvectors of matrices. Real world problems are modeled and solved using whatever methods are appropriate - paper and pencil, graphing calculator or computer algebra systems. Prerequisite:
MAT 136.

MAT 277 Algebra: Functions and Modeling (3)
This course includes topics related to the NCTM K-8 curriculum in algebra, number theory, data analysis and problem solving. Mathematics will be presented using a variety of pedagogical methods including discussion in groups, cooperative learning groups and individual and group investigation of mathematical content. One goal of the course is to make students secure in their ability to be independent learners of mathematical content. Prerequisite:
MAT 185 or consent of the instructor. Offered alternate years.

MAT 312 Advanced Geometry (3)
This course uses a formal axiomatic development to study both Euclidean and non-Euclidean geometries. The course includes a significant amount of mathematical history particularly as the discovery of non-Euclidean geometry relates to the development of modern mathematics of the past century. Formal proof is a major focus of this course. Prerequisite:
MAT 211. Offered alternate years.

MAT 332 Abstract Algebra (3)
A study of groups and rings using properties of sets, equivalence relations and number theory. Historical contributions of mathematicians to number theory and algebra are discussed, particularly those of Diophantus, Fermat, Euler, Lagrange, Abel, Cayley, Cauchy, Galois, Jordan, Noether, Germain, Artin, Dedekind and Sylow. Prerequisite:
MAT 230. Offered alternate years.

MAT 340 Probability and Statistics (3)
A study of the theory of probability and inferential statistics, including both discrete and continuous probability distributions. The distributions studied include the normal, gamma, exponential, Chi-square, t and F-distributions. Includes random sampling, estimation theory, unbiased estimators and some study of tests of hypotheses, linear regression and correlation. Historical contributions of mathematicians to number theory and algebra are discussed, particularly those of Bayes, Bernoulli, Chebyshev, Gauss and Poisson. Prerequisite:
MAT 136; MAT 225 recommended.

MAT 350 Differential Equations and Modeling (3)
A study of differential equations generated from modeling nature and the physical world using analytic, numeric, and graphical techniques. The course will begin with the study of elementary differential equations and introductory models in classroom and computer laboratory settings. Then more complex general mathematical models will be introduced. Calculator and computer technology will be used extensively. Group and individual projects will be required. Prerequisite:
MAT 136. Offered alternate years.

MAT 360 Operations Research (3)
A study of introductory topics in operations research linear programming, integer programming, network models and applications to the transportation problem and the Program Evaluation and Review Technique, Markov chains, queuing theory, and simulation. Computer technology will be used extensively. Group and individual projects will be required. Prerequisite:
MAT 230. Offered alternate years.

MAT 380 Post-Student Teaching (2)
This course includes both contents and methods. The content topics discussed are ones that can be adapted to either elementary or secondary levels and relate to "mathematics enrichment." The methods topics discussed are ones that are most meaningful only after student teaching has been completed. The course also includes topics that relate to "being a professional." Students will discuss the K-12 reform curriculum of the NCTM standards, the integrated mathematics curriculum vs. the traditional mathematics curriculum, other current trends in mathematics education and the future of mathematics education. The course will also include topics from history of mathematics.

MAT 390 Independent Study in Mathematics (3-5) (By arrangement)
Two courses of independent study in mathematics are required for graduation with honors in Mathematics; also available by proposal from any student majoring in Mathematics.

MAT 401 Analysis I (3)
This course is intended as a first course in analysis following multivariate calculus. The study of sets, sequences and mappings becomes a foundation for more theoretical study of real and complex analysis. Topics included are countable, connected, open and closed sets, convergence of sequences, continuity and uniform continuity and a first investigation of metric spaces, separability and compactness. Prerequisite:
MAT 225. Offered alternate years.


Modified 10/17/00