I've long been interested in various math related subjects (technology, philosophy, sciences, computer science, languages, etc.) without really invested time to actually any learn any of them. I probably sucks at them, as I usually fail my math and sciences when I was in secondary/high-school (I didn't pay attention in class, now I'm regret about it). And I don't really know what $a^{2} + b^{2} = c^{2}$ really means until quite recently.
Now I am more motivated and decided to spend some time to sit down and learn about them. I plan to start from math because it is more or less a foundation, or provides crucial intuition for all these subjects.
It's probably reasonable to start from secondary-school-level math though I found this learning path not interesting enough to keep me motivated. Hence I wish to get right into college-level math, but with a self-contained material that doesn't require much basic math, especially the formulas (e.g. $x=\frac{-b\pm\sqrt{4ac+b^{2}}}{2a}$, $\sin\theta=\cos(90^{\circ}-\theta)$, which I have no idea what they are). It's more preferable if these basic math can be introduce with a college-level manner (e.g. Being constructed/proved from lower level concepts). After some Googling I've found this book (Comprehensive Mathematics for Computer Scientists that provides general introduction to college-level math with, hopefully, reasonable dificulty for me.
The book basically build up a comprehensive portion of computer science related math ("including sets, numbers, graphs, algebra, logic, grammars, machines, linear geometry, calculus, ODEs, and special themes such as neural networks, Fourier theory, wavelets, numerical issues, statistics, categories, and manifolds" [quoted from Amazon]) from propositional logic and axiomatic set theory, without going deep into the details of these constructions (e.g. "it discusses graph theory, but does not mention the graph coloring problem or the shortest path problem" [quoted from an Amazon review]).
So my questions are:
- Are this book suitable for my needs in the way that it:
- Reintroduce basic math so that one can reinforce his/her foundation.
- Self-contained to the extent that minimal to none previous mathematical background is required.
- Provides a good coverage of introductory college-level math which serves as a sound foundation for further study of more advanced undergraduate subjects.
- What level of math (e.g. first term of pure math major, first year of computer science math) can someone obtains given that he/she absorbed a reasonable portion of this book?
- How many hours should someone with poor to no math foundation expect to get through it?
- What other books, series, or lectures do you suggest? And
- What level of math can be archived going through it?
- How long will it takes?
Best Answer
It seems that you are looking for mathematics that is not too technical. In this regard, I do recommend the textbook 'Comprehensive Mathematics for Computer Scientists' because it contains the type of theory that forms the foundations of mathematics - i.e. sets and logic - without going into numerical analysis. Logic and set theory can be intuitive and fun and is definitely useful for application in other subjects such as computer science and philosophy.
On the other hand, theoretical mathematics that is abstracted from numbers, such as linear algebra (chapters 20 -25), can be difficult to master if you are not dedicated, as there are many complicated concepts to understand. For a student with no math foundation, many of the chapters in this textbook will be fast-paced.
If you are looking to "reintroduce basic maths", then this book is not suitable. A better textbook would be one that is aimed at high-school students or a first-year introductory course. The level of math that you will be at once you have mastered the book will be about the end of a second-year pure maths course at university. You can expect to require 5 hours per week for a year $\approx$ 250 hours in total.
An alternate solution, which is a "self-contained" book and requiring "minimal to no previous mathematical background" is to find a descriptive coffee-table style book on mathematics, such as 50 mathematical ideas you really need to know by Tony Crilly (London: Quercus). In my opinion, the more description that the book gives and the fewer formulae, the easier it is to understand what is going on. This book can easily be read by dipping into and out of different chapters, which each take about half an hour to read and understand (there are 50 chapters).