Foundations What's a good book for last year of A levels Maths?

AI Thread Summary
The discussion centers on finding self-study resources for Mathematics in preparation for the final course of Bachillerato. The individual has recently excelled in Mathematics, achieving a top score, and is motivated to continue studying independently over the summer. Key topics to cover include Linear Algebra, Calculus (derivatives and integrals), and Geometry, with a particular interest in introductory Combinatorics. The individual is comfortable with fundamental concepts in these areas and is looking for accessible, ideally free, resources. MIT's "scholar" courses are suggested as suitable options, particularly for topics like Single Variable Calculus. There is also a request for assistance specifically with Geometry and Combinatorics resources, emphasizing a preference for open-source materials over downloads. Public libraries are mentioned as a resource for accessing materials.
PhysicsLad
Messages
21
Reaction score
2
I'm looking for a book to self-study this summer before my last course of Bachillerato (A Levels or High School in other countries).

My performance in Mathematics has only improved and I've just been given the maximum mark this last term (10/10 or A+). This has motivated me a lot to keep studying on my own before attending classes again (in September).

The course content that I need to study is composed by the following:

- Linear Algebra (matrices, determinants, linear equation systems, Cramer's rule)
- Derivatives and Integrals (applications of Calculus, Rolle-Lagrange-Cauchy-l'Hopital, definite and indefinite integrals)
- Geometry (vector space, points planes and lines, positions...)

I'm comfortable at playing with real numbers, doing essential derivative stuff (Chain rule and so on), solving limits. I know basic trigonometry and 2d plane geometry, introductory Statistics and Probability, typical imaginary numbers stuff, binomial theorem, solving basic systems with Gauss method...

The book would ideally be free but I can always access it anyway, if you know what I mean. I will study Physics at uni after this course. If you can point me out some introductory Combinatorics it's a big plus...
 
Physics news on Phys.org
MIT has courses meant for high-schoolers, the "scholar" versions. Search for "MIT Scholar" and you'll find what you need.

PS. I notice what you must learn is not that deep, for example Taylor's theorem is not included. So these scholar courses are probably at the right level for you.
 
Last edited:
  • Like
Likes PhysicsLad
Thank you. I'm taking a look at the Single Variable Calculus lectures.
 
Anybody?
 
You've been helped, young man. And asking for books that you can download anyway is asking for trouble.
 
Aight, I was just hoping somebody would help with the Geometry and Combinatorics part (I didn't find info about these on MIT).

Where did I mention downloads though? There are plenty of public libraries here:biggrin: (I just prefer open source for readiness and personal preference)
 

Thread '"WHAT IS A QUANTUM FIELD THEORY?" A First Introduction for Mathematicians'

The book is fascinating. If your education includes a typical math degree curriculum, with Lebesgue integration, functional analysis, etc, it teaches QFT with only a passing acquaintance of ordinary QM you would get at HS. However, I would read Lenny Susskind's book on QM first. Purchased a copy straight away, but it will not arrive until the end of December; however, Scribd has a PDF I am now studying. The first part introduces distribution theory (and other related concepts), which...
View full post »

Thread 'Books with a more theoretical approach to turbulence and DNS'

I've gone through the Standard turbulence textbooks such as Pope's Turbulent Flows and Wilcox' Turbulent modelling for CFD which mostly Covers RANS and the closure models. I want to jump more into DNS but most of the work i've been able to come across is too "practical" and not much explanation of the theory behind it. I wonder if there is a book that takes a theoretical approach to Turbulence starting from the full Navier Stokes Equations and developing from there, instead of jumping from...
View full post »

Similar threads

What would be a good book for learning Linear Algebra by myself?
Replies
12
Views
7K
Intro Math Are the (translated) High School Japanese maths textbooks by Kodaira Good?
Replies
15
Views
4K
Intro Math Plan to revise my learned math & start learning pure math
Replies
5
Views
4K
Calculus Which books for Calculus AND Linear Algebra
Replies
4
Views
3K
Classical Source recommendation on Differential Geometry
Replies
6
Views
3K
  • Sticky
Other Collection of Free Online Math Books and Lecture Notes (part 1)
Replies
16
Views
10K
Intro Physics Level of Math Required for Young’s University Physics
Replies
11
Views
4K
Intro Physics High School Physics and Math books for self-studying?
Replies
11
Views
6K
Classical A good book that covers everything?
Replies
10
Views
2K
Calculus Is there a good book to self study calculus?
Replies
45
Views
16K

Hot Threads

Recent Insights

Back
Top