Taking Topology and Analysis in the Fall. What should I expect?

File: 41XPgM3DpFL._SY344_BO1,204,203,200_.jpg (15KB, 228x346px) Image search: [Google]

15KB, 228x346px

>>9073380
you're welcome

>>9073384

Is this book for students who have never seen a rigorous proof in their life or is it still a good supplement either way?

>>9073388
it's not for freshmen. Well technically you could read as a freshman and still get some insight of course but it's a preparatory book for analysis, with tips for studying analysis which is what you literally asked for.
So...

read munkres

>>9073380
my fav entry analysis book is Understanding Analysis by Abott, if you are struggling in the course check it out.

File: 13386234623.jpg (63KB, 596x1024px) Image search: [Google]

63KB, 596x1024px

>>9073380

>>9073380
>first post wasn't Rudin
it's a rite of passage. read Rudin.

>>9073380
Open sets are your friend. (They always give you some "wiggle" room)

You'll see epsilon-delta definition of continuity perhaps.

Bolzano-Weierstrass

Heine-Borel

Different types of convergence criteria (Cauchy criteria (proves convergence but doesn't say to what value) vs. limit approaching some fixed L (guessed or given))

Subtle changes to quantifiers yield completely different definitions. (pointwise convergence of a seq of functions vs uniform convergence of seq of functions)

You'll learn when you can change the order of limiting operations. (Sums&Sums, Sums&Integrals, Integrals&Integrals, etc.)

Also a lot of counter-examples to intuition. (These are very helpful to keep in mind)

The subtleties of the force, young Padawan, you'll learn.

https://www.youtube.com/watch?v=xUe29YVteA4

>>9075061
I did both semesters of Advanced Calculus using
"An Introduction to Analysis" by William R. Wade

Graduate level (as undergrad btw) Real Analysis using
Rudin, Royden, and Nagy

>>9073380
This asymmetry is triggering me

>>9074860
THIS. The problems beat my fucking ass, but if you take your time, this book will help you exponentially