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Course Criteria
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3.00 Credits
In this course students are guided in exploring the nature of fractal geometry and experiencing the ideas of chaos. Topics covered include the Chaos Game, dimension, iteration and asymptotic behavior, bifurcation, the Butterfly Effect, complex numbers, Julia sets, the Mandelbrot set, the collage theorem, and Newton's Method.
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3.00 Credits
This course introduces the student to the many ways in which mathematicians address the concept of infinity. Early Pythagorean notions about infinity and irrational numbers and their gradual evolution into the real number and limit concepts by nineteenth century mathematicians are examined. The course then explores Cantor's ground-breaking work in set theory, in which the infinite is regarded as a completed whole, capable of precise analytic description.
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3.00 Credits
A survey of mathematics from the Ancient Greeks to the modern day through looking at its great ideas and theorems. Topics vary, but may include the Pythagorean theorem and Euclidean geometry, number theory, Cardano's solution of the cubic, Newton's discoveryof the calculus, mathematical modeling, abstraction and proof, and probability and statistics.
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3.00 Credits
Non-Western and non-European influences played a key role in the development of many important mathematical concepts. This course traces these influences, from the earliest emergence of counting and number systems up to the Arab influence on the foundations of algebra. Topics include mathematics of the Incas, Mayans and Yoruba people; Egyptian and Babylonian mathematics; Chinese and Indian mathematics; and the mathematics of the Arabs.
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3.00 Credits
An introduction to axiomatic plane geometry. Topics include points, lines, angles, triangles, circles, and geometrical transformations. Other possible topics include solid geometry, projective geometry, hyperbolic and spherical geometry.
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3.00 Credits
An introduction to the mathematical techniques used to explore, model, and analyze phenomena in the biological and earth sciences. Topics include probability theory, exponential growth and decay, stochastic modeling, regression and Markov models, optimization, periodic functions, rates of change, graphical analyses, and asymptotic behavior of functions. In many instances, real data drawn from the biological and earth sciences will be used to develop, implement and analyze the models.
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3.00 Credits
A hands-on introduction to the concepts and practice of cryptology. The mathematics, computer science, ethics, and law of cryptography and cryptanalysis are studied. Topics include confidentiality, data integrity, authentication, data encryption and decryption, ciphers, and digital signatures. Number theory, statistics and algebra are utilized throughout the course. Applications in areas such as health insurance, virtual business, and sending secure e-mail are introduced.
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4.00 Credits
A first calculus course designed for majors in mathematics and the physical sciences. Topics include limits, continuity, differentiation, applications of derivatives, antidifferentiation, the definite integral, and the Fundamental Theorem of Calculus. Prerequisite: MS101
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4.00 Credits
The continuation of MS201. Topics include techniques of integration, applications of integration, differential equations, sequences and series, power series, and Taylor's theorem. Prerequisite: MS201
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4.00 Credits
Calculus of more than one variable. Topics include vectors, parametric equations, polar coordinates, partial differentiation, multiple integration, and vector fields. Prerequisite: MS202
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