The Final (write the solutions VERY CAREFULLY, as if you are publishing them in a professional journal; sumbit electronically; due date: early Morning after the last exam).
Notes on Homological Algebra
Notes on Category Theory
Homework assignment (due Nov 22): study Chapters 6 (in great detail) and Chapter 7, and do the exercises in Chapter 6 only (currently numbered 42-54).
Homework assignment (due Nov 15): study Chapter 3 on the Cone Construction, Sections 4.1-4.4, and new (and growing) Chapter 6 on “projectives” in categories of chain complices, in the Notes on Homological Algebra and do all Exercises in Chapter 3 and in Section 4.1-4.4 (there are just a few). Expect that the notes on Homological Algebra will be growing in the next days, so check from time to time the version uploaded and download a new version when it is posted. We are now very close to finalize preparations for the central issue of Homological Algebra, i.e., the problem of “homological equivalences” (i.e., quasiisomorphism). New material often requires that some earlier parts of the notes are augmented and sometimes changed.
Homework assignment (due Nov 8): study new chapter in the Notes on Category Theory (Exactness and the formalism of points) and do the exercises in this section as well as related newly added Exercise 1 ; study pages 25-31 (Section 8) of An introduction to exact categories and do the exercises in Section 8.
Homework assignment (due Nov 1): study pages 1-19 (first 5 sections) of An introduction to exact categories in a follow up to my Thursday lecture, and do the exercises in those 5 sections.
do new exercises on pages 3-4, 37-39, 86-87 , 96 (these are the pages in the most up-to date version of the Notes on Category Theory where most of additions and changes occurred, reflecting what we have been covering recently in class). Additionally, do Exercises 1-8 in the iNotes on Homological Algebra
Homework assignment (due Oct 25): do new exercises on pages 3-4, 37-39, 86-87 , 96 (these are the pages in the most up-to date version of the Notes on Category Theory where most of additions and changes occurred, reflecting what we have been covering recently in class). Additionally, do Exercises 1-8 in the iNotes on Homological Algebra
Homework assignment (due Oct 20, Thursday): do new exercises on pages 3-4, 33-38, 83-104 (these are the pages where most of additions and changes occurred, reflecting what we have been covering recently in class).
Math 253
Homework assignment (due Oct 11): do Exercise 34 on p.34, study Sections 3 (pp.35-47) and do the exercises; and new material in Section 7 (former Section 6, pp.79-94), and do the new exercises.
Math 253
Old homework assignmentis: (due Oct 4) Study Section 6 (pp.65-73) and do the exercises. Review the material of Section 2 (pp.13-23).
Math 253