2019.1 Topology

Schedule:246T12 [13h00–14h40]
Duration:13-May-2019 – 29-Jun-2019
Classroom:B203
Study group: Telegram, link on SIGAA (soon)
Contact:thanos@imd.ufrn.br
Office:A225
Office hours:send email to book (first try to discuss your question on the study group)

Contents

Soon.

Prerequisites

This course demands a good understanding of—what I consider to be—the important topics of FMC1–FMC2 (but see below if you haven't passed FMC2 yet). To enroll, a student should be comfortable with (most of):

  • common mathematical language and notation;
  • writing and reading mathematical proofs in natural language (English and Portuguese);
  • elementary notions of mathematical logic: syntax and basic semantics of FOL;
  • very good understanding of sets, functions, relations; [12,13,15]
  • elements of order theory: posets; lub/glb (sup/inf); wosets (well ordered sets); product orders; etc.; [22]
  • limits of sequences of real numbers; [20]
  • continuity of real functions;
  • definitions by recursion and proofs by (nested) induction(s), at the very least on the natural numbers; [11]
  • algebraic structures; group theory in particular; [17,18,19]
  • infinite sets: cardinal and ordinal numbers; countable and uncountable sets; [21]
  • Russell's paradox; and ZF should at least ring a bell; [33]
  • etc.!

Numbers [in brackets] refer to chapters of fmcbook.

Especially about Chapter 11 (this is mandatory studying!) you can also watch the corresponding lectures of FMC2, 2018.2 on YouTube (the first three lectures on that playlist).

Please do read the links on mathematical writing and style on the Bibliography as well.

Students who have not passed FMC2 yet

During the first two thirds (unidades) of FMC2 I cover most of the common prerequisites mentioned above, so if you are taking FMC2 on this semester, you should still be able to enroll in this topics course as well. (But do heed the warning above.)

Level

WARNING! This will be a fast-paced and quite demanding course on the student's part. In the 2+ months that we have before the lectures start I will give pointers and help enrolled students brush up possibly rusty prerequisites via the study group.

Bibliography

Principal

(Heard of libgen.io?)

Soon.

Auxiliar

  • Eu: Matemática fundacional para computação [fmcbook]
  • Moschovakis: Notes on set theory [NST]
  • Goldrei: Classic set theory, for guided independent study (7, 8)
  • Simmons: Introduction to topology and modern analysis
  • Munkres: Topology
  • Willard: General Topology
  • Jänich: Topology
  • Gelbaum & Olmsted: Counterexamples in Analysis
  • Steen & Seebach: Counterexamples in Topology
  • Vickers: Topology via Logic

Hints

Exams

Probably your grade will be 50pts from homework and 50pts from a final written exam. Or something like that. It will depend on the topic selected as well.

Extra points

No extra points yet.

Homework

13/03/2019

  1. Estudar o capítulo 1 de [Simmons] e resolver todos os seus problemas.

Log

The course hasn't even begun yet.

Future (fluid)

13/05/2019

15/05/2019

17/05/2019

20/05/2019

22/05/2019

24/05/2019

27/05/2019

29/05/2019

31/05/2019

03/06/2019

05/06/2019

07/06/2019

10/06/2019

12/06/2019

14/06/2019

17/06/2019

19/06/2019

21/06/2019

26/06/2019

28/06/2019

Last update: Wed Mar 13 21:11:12 -03 2019