MATHEMATICS 602: Mathematical Principles in Science II
WI 2012, sections 9:30 a.m. and 2:30 p.m. MWF
Instructor: Dr. Rodica D. Costin,
Office: 436 Math Tower
Office hours: Monday, Friday 10:30-11:20 a.m. or by appointment
e-mail: costin dot 10
Review of main concepts of Math 601 needed this quarter.
Friday Jan. 5: Sections 2.1,..., up to, and including 2.5 in the notes Chapter I. Self-adjoint Matrices posted on Carmen.
Please review the notion of iner product and examples.
Jan. 9: Sections
2.7, 2.8, 2.9
Homework 1 (due Wednesday Jan. 18, since there are no classes on Monday Jan. 16)
answers must be justified. Quote a theorem and
state why it applies, or give an thorough argument (a proof).
Include all calculations, or attach a computer output to your
explanations. Even when the question askes for a yes or no answer,
justification is needed: if it is true give a proof or quote a
theorem and why it applies, or, if it is false, give a
counterexample, or show that the object does not satisfy all the
conditions of a definition etc.
An answer alone does not earn full credit!
Note. If a problem is
stated in n dimensions, you may wish start thinking about the
problem in 2 dimensions, then in three dimensions, to get a
feeling on what is going on. But a full solution to your problem
must be worked out in n dimensions.
Jan. 11: We
finished Sec. 2.9
, then did Sec. 2.10, and from 3.1 up to Theorem 25 (including).
Jan. 13: Sec. 3.1, 3.2, we reviewed the binomial
and multinomial formulas.
Homework 2 (due Monday Jan. 23)
Jan. 18: Sec. 3.3, 3.4, 3.6, 3.9
Jan. 20: Sec. 3.8.1, 3.8.2 (but we did not
discuss logs and radicals yet)
Monday Jan. 23: Sections 3.8.2 continued, started 4.1 (definition of a quadratic form)
Homework 3 (due Monday Jan. 30)
Jan. 25: Section
My office hours will run Mon, Fri
from 10:40 a.m. until noon from now on (for those of
you who have a class at 10:30)
Jan. 27: Sections
4.1 (finished), 4.2
Homework 4 (due Monday Feb. 6)
Jan. 30: Sections
Feb. 1: Sections
Feb. 3: Sections
5 ( not due
New: due Friday Feb.
17 (by popular demand)
Feb. 6: Sections
Feb. 8: Sections
Feb. 10: Sections
5.4, and we started SVD: the adjoint of a rectangular matrix,
that MM* and M*M are positive semidefinite
and have the same nonzero eigenvalues, the statement of Theorem 1 (p. 3) (The SVD decomposition).
The SVD song. Thank you, Mark!
Feb. 13: SDV
Feb. 15: Pseudoinverse.
Review of vector spaces, inner products. Countabe sets.