Math 2243 and either Math 2283 or 3283 (or their equivalent).
Students will be expected to know calculus and linear algebra (e.g. familiarity with determinants and eigenvalues is expected),
and be ready to read, understand and write proofs.
|Instructor:||Victor Reiner (You can call me "Vic").|
|Office: Vincent Hall 256
Telephone (with voice mail): 625-6682
|Classes:||Mon-Wed 2:30-4:25pm in Vincent Hall 113|
|Office hours:|| Monday 4-5pm (i.e. right after class),
and by appointment.
|Required text:||Modern graph theory by B. Bollobas, (1998, Springer Graduate Text in Math 184).|
Graphs are networks of vertices (nodes) connected by edges.
They are interesting objects in mathematics, but also usefully
model problems in computer science and optimization.
This is a first course in graph theory, emphasizing a broad collection of some of classical topics, such as
|Title||Author(s), Publ. info||Location|
|Introduction to graph theory||D. West, Prentice Hall 1996||On reserve in math library|
|Graph theory||R. Diestel||The author's download page|
|Graph theory with applications||J.A. Bondy and U.S.R. Murty||The authors' download page|
|Schaum's outlines: graph theory||V. K. Balakrishnan||On reserve in math library|
|A course in combinatorial optimization||A. Schrijver||The author's download page|
|Discrete math in statistical physics||M. Loebl||On reserve in math library|
There will be 5 homework assignments due usually every other week, but
I encourage collaboration on the homework, as long as each person understands the solutions,
writes them up in their own words, and indicates on the homework page their collaborators.
The take-home midterms and final exam are open-book, open-library, open-web,
but in contrast to the homework on exams, no collaboration or consultation of human sources is allowed.
Late homework will not be accepted. Early homework is fine, and can be left in my mailbox
in the School of Math mailroom near Vincent Hall 105.
Homework solutions should be well-explained-- the grader is told not to give credit for an unsupported answer.
Complaints about the grading should be brought to me.
|Grading scheme :||
|Assignment or Exam||Due date|| Problems from Bollobas text,
unless otherwise specified
|Homework 1||Wed, Feb. 8||
Chap. I # 1,2,3,7,17,18,19,24,26,35,38,85,94
(Typo corrections in #94:
the calligraphic "F" should be a calligraphic "T",
and it should say "diameter at most n-1", not n-2)
|Homework 2||Wed, Feb. 22||Chap. III # 12,18,19,28,40,41,82|
|Exam 1||Wed, Feb. 29||Here is Midterm 1 in PDF.|
|Homework 3||Wed, Mar. 21||
Chap. III # 1, 14, 54, 56
Chap. V # 1,3,5,23,24
(add the hypothesis that G is bridgeless to #23)
|Homework 4||Wed, Apr. 4||
Chap. V # 45,46,47,49 (#72 was removed)
Chap. VI # 1,2
Chap. VII # 1,2,3,4,6
|Exam 2||Wed, Apr. 11||Here is Midterm 2 in PDF.|
|Homework 5||Wed, Apr. 25||
Chap. II # 2,6,45
(removed Chap. II #37, and all the Chap. IX problems)
Chap. X # 1,2,4,17,42
|Final Exam||Wed, May 2||Here is the Final exam in PDF.|
|Electric networks, random walks||P.G. Doyle and J.L. Snell||Random walks and electric networks||arXiv version|
|Probabilistic method||N. Alon and J. Spencer||The probabilistic method||Wiley-Interscience, 2000|
|Surfaces and graphs on them||W.S. Massey||(Chap. 1 of) Algebraic topology: an introduction||Springer-Verlag Graduate Texts in Math 56|
|P. Giblin||Graphs, surfaces and homology||Cambridge Univ. Press 2010|