Math 647 FALL 2017, List of lectures
On this page I will post content of all lectures with reference to the
book. All handouts also will be posted here.
Monday, September 25: Review: Set Theory and Linear Algebra. Chapter 1.
Find your homework!
Reading assignment: read Chapter 1 of the book. Find on the web and read a proof
of: Axiom of Choice implies Zorn's Lemma.
Wednesday, September 27: Definition of category. Examples. Sections 2.1-2.2.
Friday, September 29: Functors. Section 2.3.
Monday, October 2: More of functors. Section 2.3.
Wednesday, October 4: Natural transformations of functors. Section 2.4.
Friday, October 6: Equivalences of categories. Section 2.5.
Representable functors and Yoneda’s Lemma. Section 2.6.
Monday, October 9: More on equivalences of categories.
Representable functors and Yoneda’s Lemma. Sections 2.5-2.6.
Wednesday, October 11: Initial and terminal objects; products and
coproducts. Sections 3.1-3.2.
Friday, October 13: Universal properties and quotients. Section 3.3.
Monday, October 16: Fractions. Reflection in a functor. Universal objects.
Wednesday, October 18: More universal objects. Generators and relations.
Friday, October 20: Adjoint functors. Section 3.8.
Monday, October 23: More on adjoint functors. Section 3.8.
Reading assignment: read Section 3.7 and Theorem 3.8.15 in the book.
Wednesday, October 25: Tensor product of vector spaces. Section 4.1.
Friday, October 27: Tensor algebra. Section 4.2.
Monday, October 30: Symmetric algebra and symmetric powers. Section 4.2.
We will have MIDTERM on Friday!!!
New Homework (due on Wednesday)!
Wednesday, November 1: Exterior algebra and exterior powers. Section 4.3.
Friday, November 3: MIDTERM. Here are solutions.
Monday, November 6: Determinants via top exterior power. Section 4.3.
Wednesday, November 8: Bilinear forms. Section 4.4.
Friday, November 10: More on bilinear forms. Section 4.4.
Reading assignment: read about Hermitian forms in the end of Section 4.4.
Monday, November 13: Jordan-Holder series and presentations. Section 6.1.
Wednesday, November 15: Class was cancelled.
Friday, November 17: Cyclic, symmetric and alternating groups. Sections 6.2-6.4.
Monday, November 20: Some linear groups. Section 6.5.
Wednesday, November 22: Symmetry groups, free products.
Last Homework (due on Friday)!
Monday, November 27: Semidirect products.
Wednesday, November 29: Group actions.
Friday, December 1: Examples of permutation groups. Section 7.2.
Reading assignment: read Example 7.2.16 in the book and find mistake there.
Tuesday, December 5: FINAL EXAM. Here are solutions.