MATH 3810, Complex Variables
MWF: 9:05 - 10:00 a.m., BR 112

Prerequisite: "C" or better in MATH 2110.

Course description (from the catalog): Complex numbers, calculus of complex variables, analytic functions, Cauchy's Theorem, series, the Residue Theorem, and applications. Lec. 3. Cr. 3.

Course objectives (from the departmental syllabus): To enable the student to obtain an understanding of the basics of complex analysis and its applications.

Textbook: John M. Howie, Complex Analysis, Springer (2007))

Topics: Complex numbers, complex functions, complex differentiation, analytic and harmonic functions, complex integration, and infinite series representations.

MATH 4120, Advanced Calculus II
MWF: 10:10 - 11:05 a.m., Th: 10:00 - 10:55, BR 420

Prerequisite: "C" or better in MATH 4110

Course objectives (from the departmental syllabus): One of the main objectives of the course is to bridge the gap between undergraduate calculus to graduate courses by giving rigorous treatment of topics like real number system, sequences and series, continuity, differentiation, integration in one and higher dimensions, and uniform convergence.

Textbook: Walter Rudin, Principles of Mathematical Analysis, McGraw-Hill; 3rd edition, 1976.
Recommended Text: Bernard R. Gelbaum and John M. H. Olmsted, Counterexamples in Analysis, Dover Publications; 2003

Topics: The Riemann-Stieltjes integral, sequences and series of functions, functions of several variables, special functions, Lebesgue integral.

MATH 4620, History of Mathematics II
MWF: 12:20 - 1:15 p.m., BR 306

Prerequisite: "C" or better in MATH 3400 or consent of instructor.

Course description (from the catalog): History of mathematics from the beginnings of calculus through the modern times.

Course objectives: To show the development of mathematics over the ages.

Textbook: Victor J Katz, A History of Mathematics, an Introduction, Addison Wesley; 3 edition (2008).

Topics: Analytic Geometry: Descartes, The Invention of Projective Geometry, Calculus: Newton and Leibniz, Development of Algebra, Development of Analysis; e-d definition of the limit, complex analysis, etc., Probability theory, Number theory: Fermat, Euler, Gauss, Non-Euclidean geometry, Set theory and topology, Other Topics

Additional Resources:

• Oystein Ore, Number Theory and its History, Dover 1988
• Lucas N. H. Bunt, Philip S. Jones, Jack D. Bedient, The Historical Roots of Elementary Mathematics, Dover, 1988
• Robert Kaplan, The Nothing That Is, A Natural History of Zero, Oxford University Press, 1999
• Petr Beckman, A History of Pi, Dorset Press, 1989 or St. Martin's Griffin, 1976
• Robert Kaplan and Ellen Kaplan, The Art of the Infinite, The Pleasures of Mathematics, Oxford University Press, 2004
• Jadran Mimica, Intimations of Infinity, The Cultural Meanings of the Iqwaye Counting Systems and Number, Berg Publishers Ltd., 1988
• Peter French, John Dee, The World of Elizabethan Magus, Dorset Press, 1989
• John McLeish, The Story of Numbers, How Mathematics Has Shaped Civilization, Ballantine Books, 1994
• Karl Menninger, Number Words and Number Symbols : A Cultural History of Numbers, Dover Publications, Reprint edition, 1992.
• Ivor Grattan-Guinness, The Rainbow of Mathematics: A History of the Mathematical Sciences, W. W. Norton & Company, 2000.
• E. G. Richards, Mapping Time: The Calendar and Its History, Oxford University Press, 2000