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Is calculus enough?

- Thread starter JayC
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Is calculus enough?

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quasar987

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great news! Can you also suggest a textbook ? I've heard many people say topology by Munkres is the best one.RandR^n and metric spaces first (as seen in elementary analysis courses), then the basic definitions of topology are going to be hard. In the sens that they will seem ferociously abstract and unmotivated.

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Two good introductory books

A light hearted but mathematically sound overview

( watch out for the hairy ball theorem )

Surface Topology by P A Firby and C F Gardiner

A small more rigouous but easy to follow introduction

Introduction to Metric and Topological Spaces

By W A Sutherland

A light hearted but mathematically sound overview

( watch out for the hairy ball theorem )

Surface Topology by P A Firby and C F Gardiner

A small more rigouous but easy to follow introduction

Introduction to Metric and Topological Spaces

By W A Sutherland

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quasar987

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That said, I recommend the book 'Introduction to Topological Manifolds' by John M. Lee, chapters 2-3-4 and also Bredon's 'Topology and Geometry' chapter 0. Or course, you can also bring Munkres along but Lee should be your flashlight.

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Great suggestions. Thanks

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1. A proofs class or

2. A logic class and knowledge of sets

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The first chapter in the Topology by Munkres, covers pretty much everything you need to know on set theory and that will be essential in topology.

1. A proofs class or

2. A logic class and knowledge of sets

But i do agree that a proofs class is essential, or simply mathematical maturity for that matter. It is sad to see how some of my classmates struggle when it comes to proofs and the like. Not all of them of course, only the people who thought taking Topology as their first rigorous (strictly proof-based) course was a good idea.

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