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Course Criteria
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4.00 Credits
This course is designed to introduce students to the concepts and methods of higher mathematics. Techniques of mathematical proof are emphasized. Topics include set theory, relations, functions, countable and uncountable sets and others selected by the instructor.
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3.60 Credits
A study of the work of four major Spanish painters, each of whom is considered the greatest painter of his period in Spain: El Greco (Renaissance), Velazquez (Baroque), Goya (Neoclassicism/ Romanticism), Picasso (20th century). The course includes a weekly class in one of the museums in Madrid such as the Prado, the Reina Sofia and the Thyssen collection.
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4.00 Credits
A unit course emphasizing spoken and written Spanish skills. The course is designed to help students achieve and maintain the linguistic skills needed for the program's other courses and for personal and professional activities. Required for program participants.
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4.00 Credits
Continuation of Spanish 301S. Required for program participants.
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4.00 Credits
A rigorous introduction to fundamental concepts of real analysis. Topics may include sequences and series, power series, Taylor series and the calculus of power series; metric spaces, continuous functions on metric spaces, completeness, compactness, connectedness; sequences of functions, pointwise and uniform convergence of functions. Prerequisites: Mathematics 205 and 280. Offered in fall semester.
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4.00 Credits
Topics include algebra, geometry and topology of the complex number field, differential and integral calculus of functions of a complex variable. Taylor and Laurent series, integral theorems and applications. Prerequisites: Mathematics 205 and 280. Offered in spring semester.
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4.00 Credits
An introduction to the abstract theory of groups. Topics include the structure of groups, permutation groups, subgroups and quotient groups. Prerequisite: Mathematics 280. Offered in spring semester.
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4.00 Credits
An introduction to the abstract theory of algebraic structures including rings and fields. Topics may include ideals, quotients, the structure of fields, Galois theory. Prerequisite: Mathematics 280. Offered in fall semester.
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4.00 Credits
An introduction to modern mathematical logic, including the most important results in the subject. Topics include propositional and predicate logic; models, formal deductions and the G?el Completeness Theorem; applications to algebra, analysis and number theory; decidability and the G?el Incompleteness Theorem. Treatment of the subject matter is rigorous, but historical and philosophical aspects are discussed. Prerequisite: Mathematics 280. Also offered as Computer Science 317 and Philosophy 317.
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4.00 Credits
Graph theory deals with the study of a finite set of points connected by lines. Problems in such diverse areas as transportation networks, social networks and chemical bonds can be formulated and solved by the use of graph theory. The course includes theory, algorithms, applications and history. Prerequisite: Mathematics 217 or 280. Also offered as Computer Science 318.
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