My Journey Through First Ten Chapters of Spivak’s Calculus

goepigen
9 min readApr 16, 2022

376 hours, 293 problems, 335 pages written

Photo by Kayaan Udachia on Unsplash

In life, many times memories of challenging times are sweet, or at least bittersweet. As I push through the challenge of completing every problem in Michael Spivak’s Calculus, I can already imagine how the memories about each of the first ten chapters I have successfully completed so far will feel in many years time: sweet.

I don’t remember exactly how I stumbled across someone mentioning this particular calculus book. I just know that when I did, I started researching more about the book and other books like it, and pretty much everything I remember reading about it indicated that it was legendary among anyone interested in mathematics — students, teachers, hobbyists, etc.

I’m going to give you a very quick rundown of the first ten chapters and my general thoughts on them. No specific details on problems or an in-depth look. Just impressions in case you yourself are thinking of braving the challenge and want to get a notion of what awaits you.

Here you can see all my work so far.

But first, let me give you a few numbers that may be called “fun facts” about my journey so far:

  • Problems and pages written to solve problems, by chapter:
    Ch 1: Basic Properties of Numbers, 25, 25 pages
    Ch 2: Numbers of Various Sorts, 28, 33 pages
    Ch 3: Functions, 28, 24 pages
    Ch 4: Graphs, 23, 28 pages
    Ch 4 Appendix I: Vectors, 7, 6 pages
    Ch 4 Appendix II: Conic Sections, 3
    Ch 4 Appendix III: Polar Coordinates, 10, 11 pages
    Ch 5: Limits, 42, 54 pages
    Ch 6: Continuous Functions, 17, 23 pages
    Ch 7: Three Hard Theorems, 21, 32 pages
    Ch 8: Least Upper Bounds, 20, 36 pages
    Ch 8: Appendix I: Uniform Continuity, 4, 5 pages
    Ch 9: Derivatives, 30, 18 pages
    Ch 10: Differentiation, 35, 40 pages

Therefore, approximately 293 problems done so far (I say approximately, because I left about ten or so problems for later for example I still have to do the three problems on conic sections).

This took 335 pages to complete, and 376 hours.

I did my googling about the book spread out through time. It sort of helps you to keep going when basically everyone says how great the book is and how special it is to work through the…

goepigen

Spending multiple years self-studying whatever I want. Born in 🇧🇷 grew up in the 🇺🇸, I quit my tech job in🇨🇭 to study full-time on my own.