How do I teach myself precalculus up to calculus?

[Alfie Simpson]

What are some good textbooks, websites, question papers and other sources of information that will help me teach myself precalculus up to calculus? How long will this take until I have a good grasp of the knowledge?

 

[SteamKing]

Pre-calculus is a grab-bag term for the pre-requisite subjects for learning calculus, chiefly algebra and trigonometry. No one studies pre-calculus to teach themselves pre-calculus.

If you want to do well in calculus, study basic and college algebra, trigonometry, and brush up some on geometry.

 

[micromass]

Take a look at Lang's basic mathematics. It contains everything you need to know to be able to start calculus.

 

[bacte2013]

I strongly recommend "Principles of High School Mathematics" by Allendoerfer & Oakley.

 

[KSG4592]

As someone in the same boat as you I would recommend Basic Mathematics by Lang, but there are many books out there that would work just fine. I enjoy his style. Build a solid foundation in algebra, geometry, and trigonometry before moving on to calculus. From my understanding, it isn't the calculus that has people scratching their heads; it is their weak grounding in basic algebra that holds them back much of the time.

 

[MidgetDwarf]

I second Principals of High School Mathematics by oakley. Axler's pre-calculus book is quite good, however, it is much harder than Lang.

Maybe buy Oakley and Axler since both can be had for under 15 dollars.

 

[MidgetDwarf]

Do you know geometry? If not, try Harold Jacobs Geometry : 1st or 2nd edition. avoid the 3rd.

 

[Vardaan Bhat]

Just go through AoPS Intermediate Algebra, Precalculus, and perhaps intro to geometry. You'll be set. Note: aops precalc only covers linear algebra and trig, but intermediate algebra covers the other things like conics, functions, etc.

 

[MidgetDwarf]

Just go through AoPS Intermediate Algebra, Precalculus, and perhaps intro to geometry. You'll be set. Note: aops precalc only covers linear algebra and trig, but intermediate algebra covers the other things like conics, functions, etc.

Those books teach tricks instead of understanding. Books from Lang, Oakly, Axler, and Simmons are superior. You are not going to say that Jacobs combined with Kiselev is not better than AoPS geometry book.

 

[Kalvino]

Those books teach tricks instead of understanding. Books from Lang, Oakly, Axler, and Simmons are superior. You are not going to say that Jacobs combined with Kiselev is not better than AoPS geometry book.

If you don't mind me asking, what is the name of the book by Oakley that you're talking about? I can't find a "Principles of High School Mathematics" by Oakley, but I did find a "Principles of Mathematics" book. Is this what you're talking about?
https://www.amazon.com/dp/B0000CJ70S/?tag=pfamazon01-20

 

[MidgetDwarf]

You are correct. I would pm Mathwonk, to see which edition is the better one. This is a book you will keep on your book shelf.

 

[Vardaan Bhat]

If you think that AoPS only teaches "tricks", I HIGHLY recommend you read the books. Their entire point is rigor, intuition, and application. They assemble the most challenging and versatile material for the gifted student...

 

[MidgetDwarf]

If you think that AoPS only teaches "tricks", I HIGHLY recommend you read the books. Their entire point is rigor, intuition, and application. They assemble the most challenging and versatile material for the gifted student...

They are just tricks. Any decent book beats AoPS. Have you read Kiselev? Compare Kiselev to AoPS geometry book. Which one is better written, concise, and rigorous?

You are comparing AoPS with generic 1000 page run of the mill, glossy paged textbooks. Yes, AoPS are better than those. HOWEVER, AoPS are expensive, do not dive into the theory, as say, kiselev or axler will. AoPS reminds me of Schaum's outlines. Good to feed one's belly but not fill one's hunger.

You sound like a shill judging fro

 

[Vardaan Bhat]

If he needs to be prepared for calculus, AoPS is MORE than enough. There's a reason AoPS has the biggest online olympiad math community, and there's a reason olympiad style math is coveted so highly-it enforces true understanding and application. Note that 'style' is bolded; the very topics of olympiads like functional equations may not be necessary, but many of the fundamentals are crucial to success in further mathematics ventures.

 

[Vardaan Bhat]

Looking back on what you are saying, I still think you are a bit flawed, but AoPS does take a slightly casual, less rigorous approach. Such an approach is found in different, more classical texts. However, I think AoPS is great for the gifted student shooting to learn challenging, olympiad style, and applicable material at a fundamental level, later revisiting some of the ideas with further rigour.

Sorry to make such a big discussion :P