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. New homework!
• 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. New Homework!
• 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. Sections 3.4-3.6. New Homework!
• Wednesday, October 18: More universal objects. Generators and relations. Section 3.6.
• Friday, October 20: Adjoint functors. Section 3.8.
• Monday, October 23: More on adjoint functors. Section 3.8. New Homework!
• 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. New Homework!
• Friday, November 10: More on bilinear forms. Section 4.4.