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Course Criteria
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1.00 Credits
Prereq. High school elementary algebra or ALG 051; ALG 052 concurrent - The student learns to use the right triangle and unit circle definitions of trigonometric functions, together with their graphs, to reason about the behavior of the functions and solve applied problems. She develops her analytic and problem-solving abilities using trigonometric functions to model realistic periodic phenomena.
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3.00 Credits
Prereq. High school advanced algebra/ trigonometry, or MT 123 and MT 124 - The student builds on her previous algebra knowledge (solving equations, elementary functions and their graphs) to develop deeper knowledge of mathematical functions and to use them to create quantitative models of phenomena in science, business, and everyday life. Emphasis is placed on the use of technology tools to understand, use, and apply the function concept. Problem-solving and analytical abilities are developed throughout the work of the course. This course prepares the science or mathematics major for calculus. For the elementary education student pursuing a mathematics support, this course helps her to integrate her algebra knowledge and serves as the bridge to further mathematics courses.
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4.00 Credits
Prereq. High school precalculus, advanced mathematics, or MT 148 - The student studies functions and their rates of change in the context of applied problems, using the ideas and techniques of differential calculus. Topics include derivatives of elementary functions (polynomial, exponential, rational, logarithmic, trigonometric) and their compositions in a variety of representations (graphical, numeric, and symbolic); limits; differential equations as mathematical models for changing phenomena; and antidifferentiation. The student develops her problem-solving, analytic, and communication skills by working both independently and collaboratively to understand, formulate, and solve problems from a variety of disciplines such as physics, chemistry, biology, social science, and management. Computers and calculators are used as tools for computation, communication, and exploration of mathematical ideas.
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3.00 Credits
Prereq. High school advanced algebra or MT 123 - The student explores the mathematics of discrete finite systems, employing algorithms for problem solving in these systems. Topics include set theory, equivalence relations, congruence relations, graph and tree theory, combinatorics, logic, and recurrence relations. Coursework integrates an introduction to a variety of mathematical proof techniques, including proof by mathematical induction.
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4.00 Credits
Prereq. CM 156Q or CM 176Q - This course, which integrates the learning of mathematics with methods of teaching, is designed for the student preparing to teach at the elementary school level. The student studies the mathematical structures and operations related to sets, whole numbers, integers, rational numbers, and real numbers. She uses the properties of these systems to develop algorithms for the operations defined in each of the systems. She explores the use of manipulatives and technology in building understanding of concepts. Through the study of national, state, and local standards, and contemporary mathematics curriculum projects, she learns teaching strategies. She also gains experience with professional practices such as the development of lesson plans, unit plans, and assessment instruments designed for a variety of learning styles. Throughout the course, she evaluates herself on her ability to analyze and solve problems as well as on her ability to communicate mathematics effectively.
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4.00 Credits
Prereq. MT 243 - This course builds on the mathematical knowledge and skills that the student developed in MT 243. She studies geometry and probability and statistics, and works to strengthen her mathematical problemsolving, analytic, and communication skills. She works further to explore a variety of mathematics teaching approaches at the elementary school level.
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4.00 Credits
Prereq. MT 152 - The student extends her knowledge of calculus by exploring the ideas and techniques of integral calculus. Topics include differential equations as mathematical models of changing phenomena, the definite integral and its standard applications, techniques of antidifferentiation, Taylor polynomial approximations, improper integrals, and representations of functions by infinite series. The student builds knowledge and skill using technology tools to solve problems.
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4.00 Credits
Prereq. MT 253 - The student studies the calculus of multivariate functions with emphasis on functions of two independent variables and their three-dimensional graphs. Further topics include parametric equations; conic sections; polar, cylindrical, and spherical coordinate systems; the calculus of vectors and vector-valued functions; multiple integrals; and line integrals. She continues to develop her analytic and problem-solving abilities, working purposefully on generalization skills, algorithm and formula development, and understanding and applying theorems. In individual and group work, she solves applied problems that arise from the areas of physics, chemistry, biology, management, and mathematics itself.
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4.00 Credits
Prereq. For MT majors, MT 152; for ELM/mtm majors, MT 221 - The student studies the mathematics of matrix algebra; the structure and operations of vector spaces, including use of determinants, eigenvalues, and eigenvectors; and linear transformations. She learns the basic concepts and computational procedures associated with these structures, including the use of computer and calculator technology. Linear algebra is applied to problems in areas including linear programming, graph theory, theory of games, least squares regression, linear economic models, traffic flow, and scheduling.
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4.00 Credits
Prereq. High school advanced algebra or MT 123 - The student engages in the systematic collection, presentation, and characterization of statistical information for the purpose of decision making. She develops the mathematical skills and knowledge necessary for problem solving in statistical contexts. Both descriptive and inferential statistics are studied. Knowledge of the mathematics of probability supports conceptual understanding of statistical methods. Data analysis, graphical representation, correlation, regression, and reliability and validity issues are considered. Technology tools are used.
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