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Course Criteria
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4.00 Credits
Prerequisite: MTH 201 and sophomore standing This course explores topics in geometry, rational numbers, and proportional reasoning, as students continue to examine various mathematical processes, such as inductive and deductive reasoning, creating conjectures, constructing justifications, algebraic representations, and problem-solving strategies. Issues and activities in teaching mathematics to children weave throughout the course. Liberal Education: Quantitative Reasoning (elementary education majors only).
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4.00 Credits
Prerequisite: MTH 107 Statistical Concepts and Analysis Foundational principles of probability including methods of counting and specific probability distribution and density functions; linear models including one- and two-way ANOVA with post-hoc multiple comparisons and transformations, simple and multiple linear regression including transformations and indicator variables, and logistic regression; and basic principles of sample and experimental design. The theoretical constructs of all topics will be developed and applied to real-life or realistic situations in the life and natural sciences.
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4.00 Credits
Prerequisite: MTH 140 Students use deterministic and stochastic models based on difference and differential equations to draw conclusions and make predictions about natural systems. Mathematical topics include equilibrium analysis, bifurcation, chaos, hysteresis, phase plane analysis, and numerical simulation. Models related to population ecology, population viability, predator-prey relationships, sustainable use of renewable resources, and global climate are considered. Liberal Education: Environmental Perspectives.
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3.00 Credits
Prerequisite: MTH 141 An introduction to basic probability theory including Venn diagrams, combinatorics, conditional probability, random variables, expected values and covariance, sums of random variables, discrete probability distributions, and continuous probability densities. Theoretical concepts will be applied through a variety of examples and will include the use of inferential statistic, Bayes' Theorem, Markov chains, and random walks.
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4.00 Credits
Prerequisite: MTH 141 Introduction to numerical methods used to solve problems in applied mathematics. Algorithm studied may include root finding, function approximation, numerical integration, computing eigenvalues, and solving systems of differential equations. Students will learn FORTRAN programming language to implement these algorithms and solve the problems.
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4.00 Credits
Prerequisite: MTH 141 Extreme values of functions of several variables, implicit functions and Jacobians, transformation of coordinates, derivatives of vector-valued functions, line integrals, surface integrals, Green's theorem, Stokes' theorem, thedivergence theorem.
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3.00 Credits
Prerequisite: MTH 141 Vector methods in geometry, classical theorems, coaxial systems of circles, inversion, mappings of the Euclidean plane, non-Euclidean geometry and the Poincare model, an introduction to projective geometry.
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4.00 Credits
Prerequisite: MTH 141 First order and simple higher order differential equations, Laplace transform solution of differential equations.
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3.00 Credits
Prerequisite: MTH 140 Topics include algorithms, mathematics induction, elements of set theory, graphs, trees, elementary combinatorics, difference equations, recursion, and logic. Students will learn how algorithms are implemented on computers and will write short computer programs to execute many of the algorithms studies.
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4.00 Credits
Prerequisite: MTH 141 Vector spaces, linear dependence and independence, properties of matrices and determinates, linear transformations, eigenvalues.
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