## Is Spivak calculus real analysis?

Spivak is in a way a bridge between calculus and analysis. It’s a little too rigorous for calculus, but a little too easy for an analysis course. The problem with Spivak is that it simply doesn’t treat the right topics for an analysis course. It treats the normal calculus topics.

### Does Spivak cover multivariable calculus?

Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus (1965) by Michael Spivak is a brief, rigorous, and modern textbook of multivariable calculus, differential forms, and integration on manifolds for advanced undergraduates.

**What is manifold calculus?**

Manifold calculus is a way to study (say, the homotopy type of) contravariant functors F from đť’Ş(M) to spaces which take isotopy equivalences to (weak) homotopy equivalences.

**What should I read after Spivak calculus?**

For mathematics, you could now read linear algebra or multivariable calculus. I recommend linear algebra first, since multivariable calculus will go easier with some knowledge of linear algebra. If you want rigorous books, then I can highly recommend “Linear algebra” by Serge Lang.

## What should I study after Spivak calculus?

Generally people study linear algebra after calculus. IMO real analysis is nice to have learned before learning topology as it will give a reservoir of intuition and examples, and will cover some topology along the way anyway. After spivak, apostol is redundant; it’s a better use of time to go on a real analysis text.

### What comes after Spivak calculus?

It covers the necessary linear algebra in a nice way and then goes to multivariable calculus. It covers the necessary linear algebra in a nice way and then goes to multivariable calculus.

**Is r3 a manifold?**

Real projective 3-space It is a compact, smooth manifold of dimension 3, and is a special case Gr(1, R4) of a Grassmannian space.

**Which is better Apostol or Spivak?**

While both books have complete proofs and a good emphasis on theory, Spivak’s book is better as an introduction to rigorous math because many of its problems are more difficult and theoretically oriented than Apostol’s.

## Is Apostol good for linear algebra?

Apostol’s book is really excellent, but you might find it hard going if you haven’t done linear algebra before – for instance he has a different way of defining the determinant and rank of matrices, all very rigorous, but it might seem a bit out there if you see it the first time.

### What is the hardest math class in the world?

â€śMath 55â€ť has gained a reputation as the toughest undergraduate math class at Harvardâ€”and by that assessment, maybe in the world. The course is one many students dread, while some sign up out of pure curiosity, to see what all the fuss is about.