21-241: Matrix Algebra

Schedule and Homework

This schedule is tentative. It will get more accurate as the semester progresses. No week's topics should be taken as final until the homework is linked.

Week #1:  Aug 30 - Sep. 3 Homework	Metric Spaces Compact Sets	Finite, countable infinite and uncountable sets. NxN and Q are countable, binary operations. Groups, Examples, identity and inverse elements.
Week #2:  Sep. 6 - 10 Homework	Compact Sets Connected Sets	Rings, Examples Fields, Examples, the Real numbers
	Administrative Note: Monday 6 September is Labor Day. Class will not meet.
Week #3:  Sep 13 - 17 Homework Problem Session 1	Convergent Sequences Subsequences Cauchy Sequences	Homomorphisms of groups, normal subgroups.
Week #4:  Sep. 20 - 24 Homework Problem Session 2	Series Series of Nonnegative terms The Root and Ratio Tests Power Series Summation by Parts	Quotient groups, the First Isomorphism Theorem.
Week #5:  Sep. 27 - Oct. 1 Homework Problem Session 3	Absolute Convergence Addition and Multiplication of Series Rearrangements Limits of Functions Continuous Functions
Week #6:  Oct. 4 - 8 Homework Problem Session 4	Continuity and Compactness Continuity and Connectedness Discontinuities Monotonic Functions Infinite Limits and Linits at Infinity Connected, Path Connected and Simply Connected. Homotopies and the Fundamental Group.
Week #7:  Oct 11 - 15 Midterm Problem Session 5	The Derivative of a Real Function Mean Value Theorems The Continuity of Derivatives L'Hospital's Rule Derivatives of Higher Order
Week #8:  Oct 18 - 22 Homework Problem Session 6	Taylor's Theorem Differentiation of Vector-valued Functions Sequences and Series of Functions: Discussion of Main Problem
	Administrative note: Friday 22 October is the Mid-Semester Break. Class will not meet.
Week #9:  Oct 25 - 29 Homework	Uniform Convergence Uniform Convergence and Contuinity Uniform Convergence and Differentiation
Week #10:  Nov 1 - 5 Homework Problem Session 8	Equicontinuous Families of Functions Definition and Existence of the (Riemann) Integral Properties of the Integral
Week #11:  Nov 8 - 12 Homework	Integration and Differentiation Integration of Vector Valued Functions Rectifiable Curves
Week #12:  Nov 15 - 19 Homework Problem Session 10	Set Functions Construction of the Lebesgue Measure
Week #13:  Nov 22 - 26 Homework	Measure Spaces
Week #14:  Nov 29 - Dec 3 Homework	Measurable Functions Simple Functions Integration
Week #15:  Dec 6 - 10 Homework	Comparison with the Riemann Integral Integration of Complex Functions Functions of Class L2
	Administrative note: Friday 10 December is the last day of class.
Final Exam Dec 10 - 21	The Final Exam will be a take some exam.