<p>Swarthmore's Directed Reading program is with a professor. It's Math 093</p>
<p>MATH 093/STAT 093. Directed Reading</p>
<p>Or you can do a senior thesis, also with a professor:</p>
<p>MATH 096/STAT 096. Thesis</p>
<p>Or, for non-honors majors, working with a professor on a specific topic in a directed reading/paper/oral presentation is required:</p>
<p>MATH 097. Senior Conference
This course is required of all senior mathematics majors in the Course Program and must be taken at Swarthmore. It provides an opportunity to delve more deeply into a particular topic agreed on by the student and the instructor. This focus is accomplished through a written paper and oral presentation.
0.5 credit.
Fall 2008. Hunter.</p>
<p>Or, the honors seminars typically meet for three hours once a week and go deep into a particular topic. I've put the enrollment for the seminars that were given either in the fall or the current semester. Honors seminars at Swarthmore are often graduate level work. Ideal preparation for PhD programs in most fields.</p>
<p>MATH 101. Real Analysis II (2 sections: 4 students/7 students)
This seminar is a continuation of Introduction to Real Analysis (MATH 063). Topics may include the inverse and implicit function theorems, differential forms, calculus on manifolds, and Lebesgue integration.
Prerequisite: MATH 063.
1 credit.
Spring 2009. Maurer.</p>
<p>MATH 102. Modern Algebra II (6 students/5 students)
This seminar is a continuation of Introduction to Modern Algebra (MATH 067). Topics covered usually include field theory, Galois theory (including the insolvability of the quintic), the structure theorem for modules over principal ideal domains, and a theoretical development of linear algebra. Other topics may be studied depending on the interests of students and instructor.
Prerequisite: MATH 067.
1 credit.
Usually offered spring only.
Fall 2008. Bergstrand. Spring 2009. Chen.</p>
<p>MATH 103. Complex Analysis
A brief study of the geometry of complex numbers is followed by a detailed treatment of the Cauchy theory of analytic functions of a complex variable: integration and Cauchy's theorem, power series, residue calculus, conformal mapping, and harmonic functions. Various applications are given, and other topicssuch as elliptic functions, analytic continuation, and the theory of Weierstrassmay be discussed.
Prerequisite: MATH 063.
1 credit.
Alternate years.
Not offered 2008-2009.</p>
<p>MATH 104. Topology
An introduction to point-set, combinatorial, and algebraic topology: topological spaces, classification of surfaces, the fundamental group, covering spaces, simplicial complexes, and homology (including related algebra).
Prerequisites: MATH 063 and 067.
2 credits.
Alternate years.
Not offered 2008-2009.</p>
<p>MATH 105. Probability (9 students)
Advanced topics in probability theory. Topics may include branching processes, card shuffling, the Central Limit Theorem, generating functions, the Laws of Large Numbers, Markov chains, optimal stopping theory, percolation, the Poisson process, renewal theory, and random walks.
Prerequisite: STAT 061.
1 credit.
Alternate years.
Spring 2009. A. Johnson.</p>
<p>MATH 106. Advanced Topics in Geometry (7 students)
The course content varies from year to year among differential geometry, differential topology, and algebraic geometry. In 2009, the topic is likely to be advanced differential geometry.
Prerequisites: MATH 045 and 063 or permission of the instructor.
1 credit.
Alternate years.
Spring 2009. Talvacchia.</p>