I am 22 years old and I am looking to develop my understanding and knowledge in math to be ready for Computer science related courses.

I am currently working as a software engineer (self taught). But I am interested in learning more theoretical stuff.

The problem is that I made some poor decisions when I was young and decided to go to schools that didn't teach me much math.

I bought the book "Concrete Mathematics" to get more into computer science related theory. I have been struggling a lot and have done a lot of research on why that is.

To put a label on what my state was when I started: I hadn't had any math that used letters in its equations. I hadn't touched algebra, calculus or anything you assume someone who graduates from highschool should know.

I figured this out pretty late and never knew that there was such a big world of mathematics that I missed out on.

Currently I am jumping from subject to subject. One moment I am trying to figure out what logarithms are, the other moment I am trying to figure out what complex numbers and derivatives, linear algebra or just ways to simplify equations in order to get X =.

I find it very difficult to figure out what I am lacking, especially when you have to google "What does sideways M mean in math" (Sigma). Now in this scenario Concrete Mathematics explained Sigma, but I didn't know it when I was doing my initial preparation.

Now I feel like I am in a pretty bad spot for a linear learning curve that can continue from a nice point. So I assume I will probably have to start with a good book and go from there, even if I already know half the stuff in the book. I frankly have no clue what my state is as it is not very tangible and I know very little about the world of math.

I have tried to find a book that will give me a good foundation but not be too easy for how much I already know.

I have gotten to the point of understanding second degree equations pretty well I think. The problem is also that I don't have enough practice due to there being so much stuff to catch up that my mastery of the subjects I have already caught up on mediocre to say the least. When I think I grasp a certain subject on math I move onto the next, hoping that I'll eventually have the level of math I need to do discrete math. It would also feel good to have an understanding of math that other people my age have.

Any advice is welcomed greatly. Maybe there are other people here that have been through the same experience as me and could share their method of approach?

I am okay with gaps and difficult solutions cause math wasn't the only thing I wasn't educated in and had to catch up on. But with math I just don't feel like I'm making much progress as I can't visualize a scope of what I need to know to at a good position to start with Discrete and Continuous math.

This is a list of subjects "I think" I understand enough to move past now. I am sorry of this list seems trash cause I don't really have a clue about most of the terminology or scope.

  • Simple solve for X equations / algebra (basic - intermediate??)
  • Second degree equations with ABC formula
  • Sets
  • Permutations and combinations
  • Functions
  • Equation manipulation techniques
  • Logarithms

Keep in mind that some of these have already faded in memory due to being moved past to learn new subjects. It's difficult to keep good at every single one of them without spending most of my day practicing problems in each category. I also struggle a lot to see connections between equations if there are certain steps of manipulation skipped. I generally write down every single step to manipulate a given equation due to be so inadequate.

Getting better at math might also help me become better at my job and allow me to do projecteuler projects that rely on knowledge of math to solve.

Any help is appreciated!

  • 2
    $\begingroup$ I'd recommend going to the Khan Academy website which offers good practice (for free) on everything from Pre-algebra to Calculus, Differential Equations, etc. If I were you I would go there and just started from the very basics then work through it from end-to-end. $\endgroup$ Commented May 27, 2018 at 23:13
  • $\begingroup$ Alright. Thank you. I am now trying to list out everything in khan academy i am already confident with for the sake of time. Since it's quite a lot. $\endgroup$ Commented May 29, 2018 at 22:10
  • $\begingroup$ Algebra ---> Basic Set Theory/Vendiagrams--> Basic Trigonometry and Logarithms---> Precalculus $\endgroup$
    – Quality
    Commented Jun 22, 2018 at 8:26
  • $\begingroup$ For a brief philosophical comparison between the math taught in K12 schools and the math practiced by academic mathematicians I'd advise you to watch between 2:13 and 13:58 of the following lecture. Don't mind the name of the lecture, or the parts that come before and after the time span I dilineated above. (It assumes you know in general strokes how computers are programmed and are familiar with the terms assembly language and algorithm.) $\endgroup$
    – Evan Aad
    Commented Jun 22, 2018 at 8:51
  • $\begingroup$ Does this answer your question? Learning mathematics as if an absolute beginner? $\endgroup$
    – user1147844
    Commented May 21, 2023 at 23:04

2 Answers 2


Basic Mathematics by Lang will fill in any gaps in your basic high school math.

Then use The Method of Coordinates, Functions and Graphs, Algebra, and Trigonometry, all by Gelfand, and Mathematics of Choice, by Niven, for slightly harder high-school level material. Much of the material is similar to Lang's book, but the problems are much harder.

After that, you will have a good basis to learn calculus, linear algebra and other subjects in a rigorous way.


Maybe these should help:

1) How to prove it- Daniel Velleman

2) Naive set theory - Paul R. Halmos (First 10-11 chapters)

In my opinion, 1) is a great introduction to the basic mamthematical ideas and should provide good insight on how proofs work and how they relate to set theory and logic, which are the basis for mathematics. On the other hand, 2) describes formally the construction and definition of some of the main mathematical objects and should help you with "formalism stuff". Also, I think that the book "Concrete Mathematics" that you bought (It is the one from Knuth, right?) is a great source as well!

Good Luck!

  • $\begingroup$ I think Halmos' book might be too hard for a beginner. I skimmed through it and it contains some deeper topics like axiom of choice. $\endgroup$
    – user370967
    Commented Jun 22, 2018 at 8:25
  • $\begingroup$ Yep, I should edit my answer. $\endgroup$ Commented Jun 22, 2018 at 8:34

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