Best Pre-Calculus Textbook for Depth, Problems, and Understanding?

also olympiads are very specific. to be good at IMO you need to train for IMO and learn a lot of shit. that's not a good way to learn general math at this point

>if you already had a shitty plug and chug calculus class, and you want to get correct intuitions, it might just be time you grabbed Apostol and started working through it. it's not too hard.

>if you're really interested in math I might even suggest starting analysis and linear algebra already. since you asked about linear algeba, Hoffman & Kunze is a great, serious book.

Thanks, I'll keep this in mind when I get to them.

>if you're really interested in math I might even suggest starting analysis and linear algebra already. since you asked about linear algeba, Hoffman & Kunze is a great, serious book. you don't sound like someone who would appreciate shitty "linear algebra" for engineers stuff

There's a difference between "here's the rules, here's the examples, now solve some similar problems" vs. "we're going to make you understand the basics, give you a few examples, and then you're on your own to crunch numbers and find shortcuts that will make you extremely familiar with quantitative methods". I'm interested in "Art of Problem-Solving"-style math, too.

I don't want to be an IMO competitor. I'm not looking to ace every problem. But it would be nice to be competent enough to feel comfortable with mathematical models and problem-solving to solve a commendable amount of them.

don't really understand what you mean, what are you after exactly?

which book is that?
is it in line with OP's message?

fuck

Gelfand's books are short and you could work through each of them in about a week.

>Is this as the same level as the first four books that you've suggested

No, Gelfand's books were written for gifted middle/high school kids as a supplement to their schooling. They're great for their problems that force you to understand the material and cover stuff you don't usually see in school. Marcus is a freshman linear algebra book for STEM majors.

>I got 5s in AP Calculus AB and BC
>I want to change that, starting with difficult pre-calculus problems and moving onwards to Apostol or something.

You're falling for the classic trap of being afraid of moving forward in mathematics. Usually the stuff you're shaky about will be clarified in later advanced courses. Instead of looking for a difficult precalculus book, look for a book on proofs like "A Transition to Advanced Mathematics" then study modern/abstract algebra and analysis.

>as I re-enter university

How long has it been since you last math course?

make sure you can factor anything

make sure you can PROVE trigonometric identities

make sure you know how to do basic vector problems

I'd suggest Mathematical Thinking: Problem solving and proofs

Professor Leonard on youtube has some great stuff.

>You're falling for the classic trap of being afraid of moving forward in mathematics. Usually the stuff you're shaky about will be clarified in later advanced courses. Instead of looking for a difficult precalculus book, look for a book on proofs like "A Transition to Advanced Mathematics" then study modern/abstract algebra and analysis.

I don't consider mathematics to be a linear progression of one topic to the next. After a certain point, there's horizontal and lateral development. For example, university-level calculus (I mean calc 1/2/3) is way easier than any of the pre-calculus problems you'd have to solve in problem-solving competitions until you start dealing with analysis. Unless you had a brutally hard calc 1/2/3 progression, you won't even know that you're shaky about those kinds of problems until you start hitting applied mathematical problems.

The way I see it, mathematics is about progression in two different kinds of thinking: 1) the ability to make theoretical models that build upon one another (proofing-based reasoning, i.e., found in analysis); and 2) the ability to apply theoretical understandings to practical problems (quantitative-based, i.e., applying pre-calculus, calculus, linear algebra, difEQ, etc., to solve in physics or chemistry, especially those that require creative solutions). I want to progress in both.

I appreciate your advice so far, and I will follow it, but don't mistake it for hesitance to move forward. Hell, I might work on both types at the same time, switching between the two on even and odd days.

About two years.

This is a good restatement of what pre-calculus should be about. Plus understanding the basis and the manipulations of various functions (logarithms, trigonometric functions, exponents, etc.), basic competence with matrices, vectors, and complex numbers.

>No, Gelfand's books were written for gifted middle/high school kids as a supplement to their schooling. They're great for their problems that force you to understand the material and cover stuff you don't usually see in school. Marcus is a freshman linear algebra book for STEM majors.

I meant more in terms of "breadth and depth" that I outlined in the beginning of the post, not in terms of the normal progression of mathematics.

>some combination of depth, quality/quantity of problems, and overall readability/understandability

I should probably ask tutors for their favorite textbooks because they'll know what the brainlets and what the brainmores tend to read.

Also, outside of pre-calculus, what course would cover complex number calculations that involve DeMoivre's Theorem, Euler's Identity, applications to vectors/matrices, basic combinatorics and probabilities, etc.?

Look at Cohen's precalculus book. It has challenging problems and is comprehensive, although I don't think it has probability. The book you suggested looks good too.

Cohen is another book that I considered. I don't remember why I thought Stitz-Zeager was better than Cohen, but if I can't get Stitz-Zeager, I will probably look towards Cohen. I think Cohen has more problems but less breadth... something like that. Thanks for reminding me.

>what course would cover complex number calculations that involve DeMoivre's Theorem, Euler's Identity, applications to vectors/matrices

There aren't any dedicated courses on complex numbers and geometry at that level. The topics are typically scattered throughout precaclulus, calculus, modern geometry, and complex variables. But there are books the organize the material together at your level:

Complex Numbers and Geometry by Liang-shin Hahn
Complex Numbers from A to... Z by Titu Andreescu and Dorin Andrica (More of math competition focus)
Introduction to the Geometry of Complex Numbers by Roland Deaux

Thanks for the advice. I think I'll just stick with the pre-calculus book that I found.

are you gonna waste all your time with babby tier "math" or are you gonna move on to calculus already? leithold's calculus 7 has all the precalculus you need in the appendix. DONT GET STUCK ON THE BASIC SHIT.

>Stitz-Zeager

Excellent choice. One of the more sensible uses of set theory I've seen in any textbook. A nice supplementary text which also uses a sensible approach to set theory is Richard Hammack's Book of Proof, which is free.

people.vcu.edu/~rhammack/BookOfProof/

>no one posted Basic Mathematics, Lang

This is how you know Veeky Forums is shit

Was about to post, good lad

This is what I recommend all the time. Although it is funny when people sometimes go "its too hard, this isn't for someone just learning". It's honestly one of the best books I've seen around for lower level math.

>I see some names thrown around here, like Precalculus Mathematics in a Nutshell by George Simmons and Basic Mathematics by Serge Lang, but I've found that while those books are better than your average high school fare, they're lacking according to the standards I set previously.

have you ever read OP's message?

So Veeky Forums I need to git good

I'm planning to do Apostol calculus

>read book of proof
>read a transition to advanced mathematics
>read precalculus shit if I lack something
>start doing apostol

what do you think?

Which of these 2 books is better? To do before working through a calculus book. Algebra and Trigonometry -Beecher, Precalculus - Stewart

Do you really need to post it in 2 threads + make one?

yes

econsphdtutor.wordpress.com/free-stuff/

>Read a section on the same topic in both
>Use whichever you liked more

Just emailed Stitz asking about a hard cover copy. Apparently they split it into two textbooks for printing convenience purposes. And they sell it cheaply at exactly the cost margins. Good stuff, almost makes me shed a tear.

Dumb faggots I already mentioned Basic Mathematics by Serge Lang in the original post. It's a quality textbook but it doesn't cover the basics of combinatorics AND vectors AND complex numbers AND probability, which is a dealbreaker for me. Brainlets should learn to read first before doing math.

That's a good plan, I might just steal it. Good books too. Thanks!

>I might just steal it
oh

if you find a good pdf of Apostol without fonts getting bold, thin and stuff, pls share

>pre calc
>depth

kek

>It's a quality textbook but it doesn't cover the basics of combinatorics AND vectors AND complex numbers AND probability, which is a dealbreaker for me

Just get a book for each topic. Basic combinatorics is done in any probability book worth its salt so just get Hamming's "Art of Probability". For vectors, get Schuster's "Elementary Vector Geometry" or Robinson's "Vector Geometry". And or Durell and Robson's "Advanced Trigonometry" are the best you'll find on complex numbers without it turning into full blown complex analysis.

You might be in luck. I remember I've got an Apostol pdf somewhere and it might be good. Maybe in the next hour when I'm around my computer?

I dunno what's a good way to send it or upload it

>I dunno what's a good way to send it or upload it
just upload it on mega

Just
>read a transition to advanced mathematics
>start doing Courant & John

>courant

the shitty Springer released a fuckton editions of the books. Wich one should I download/buy?

It's all the same content.

Shit I just realized that my copy has weird font too. Lol it makes it look like a book for brainlets

maybe this apostol thing wasn't a good idea

Okay bros so let's veer off topic a bit. Why the hell are Apostol, Spivak, and Courant recommended as "calculus" books? Aren't they like rudimentary analysis books that decided to cover calculus? I don't get the point or the obsession.

If you want something rigorous but don't want to miss the applications, they're your best bet.

I'm looking for kinds the same advise and also programming courses and/or youtube playlists

I just want a calculus book to explain how things work and why. For example, engineers be like "multiply both sides by dx and solve the difEQ!" while mathemaricians be like "brainlet. that's not a variable", and I have no idea what the notation really means.

What is the benefit of doing some analysis-based book instead of a particularly well-written calculus book that proved crucial theorems, provides some exercises in less important proofing, and teaches you the ins and outs of quantitative calculations with calculus?

You'll get nothing from the autistic elitists here. You are right. Stick with Stewart.

no, they aren't analysis, they're calculus
you're very confused about what a calculus book normally is. they don't prove shit, for example.

It's good practice for when you get to an actual analysis but you don't have to read a rigorous calculus book. Some people like a challenge.

I don't mind reading a rigorous calculus book. I just want to know what I'm really doing while I'm doing it so I know how to cover all of my bases and judge my level of progress.

How does this calculus book measure up?

faculty.etsu.edu/knisleyj/calculus/final.pdf

See for why:

Just do step papers and look at khan academy/Paul's notes for shit you haven't covered yet. Then move onto Slovaks calculus, artins algebra, Ireland and Rosen's number theory and rudins analysis.

As an engineer who tooK LA, how does Gilbert Strang's third edition hold up?

So, am I being too autistic if I'm going through Euler's Algebra and the Gelfand books, instead of just a precalc book like OP?

I've already taken stuff up to PDEs, but I wanted to cement my baby math knowledge

I get the feeling that what you're really looking for is in abstract algebra and number theory books.

>im interested in AOPS style math too

so why not just do the AOPS precalculus book then? It's objectively god-tier and it goes indepth, teaching you the stuff and making you prove all the major theories and tons of random-ass corollaries yourself, making sure you understand. It does probably have too much of a focus on olympiads for your taste though since some of the problems come from USAMO etc. But ya if you're looking to build just raw mathematical problem-solving/reasoning skill, AOPS books were literally made for this reason.

If you're still in high school I'd honestly do this. Problem solving is the most fun part of math honestly, couldn't give less of a fuck about analysis or topology etc.

and yes it does give you a stronger and important base, if higher math is what your end goal is

artofproblemsolving.com/articles/calculus-trap
That being said IDK how old you are, if you are already in college and just doing higher math you'll just have to roll with what you have

Get one that has a solutions manual to go with it and do a bunch of problems. You have to do problems to learn math.

Gelfand books look pretty good too, but have only skimmed through them. Lang's book looks interesting as well, but again I have only skimmed through it.

>probability, combinatorics
Literally no reason to wait desu.

>t. CS brainlet

amazon.com/Probability-Enthusiastic-Beginner-David-Morin/dp/1523318678/ref=pd_sim_14_19?_encoding=UTF8&pd_rd_i=1523318678&pd_rd_r=N5E2TC23FRPXVPDS7VYY&pd_rd_w=K70HK&pd_rd_wg=r5vS9&psc=1&refRID=N5E2TC23FRPXVPDS7VYY

for probablity self study

>he thinks combinatorics is advanced math

>AOPS
>Oh. You didn't know that the solutions are extra? Too bad.

it is. serious combinatorics is not your shitty
>HOW TO TAKE STUFF MOD P LMAO
freshman class

>literally just counting
>hard

yeahhh it is
any field of math where active research is going on is hard

There is active research in banging your mom but she's easy af.

Idk about that but im using the e-book version and have no problems. No reason to go for physical version desu, just makes navigation harder

Best statistics and probability book lads?
Undergraduate shit, preferably separate books

There is a Veeky Forums-wiki.

>no aops books in pdf

Feels bad man

Yeah I'm having the same problem unfortunately. I think AOPS might be just a brand/meme; otherwise, more people would provide free copies.

>brusing up
>on precalculus
Bruch up the 12 gauge lobotomizer, my man

i go to stanford you state school brainlet

...

That's not me, the OP. I don't go to a state school, nor do I go to the Harvard of the west. I'm a sophomore chemistry major at Harvard.

wanting the best precalculus book in the world is like buying really nice shoes for a babby

>I did fine in high school, but I hardly remember anything because it was an easy class.

Nothing amuses me more than the stupid, foolish, laughable, senseless, naive, ignorant, unintelligent and utter bullshit that brainlets come out with in order to convince themselves that they aren't what they are.

Veeky Forums-science.wikia.com/wiki/Mathematics#Probability_and_Randomness

Nah, it's actually good

Just telling it as it is. Got easy As, got 5s, etc. Maybe I am a brainlet, but at least I recognize enough to want to improve myself.

Americans need a second class to learn about basic functions

I wish I could trust your word for it. Got a snapshot of a few good pages anywhere?

Libgen has a few of their books available for download.

The books start each section with a small introduction to the topic. Then it gives you about 5-8 problems that develop the theory. Following that are detailed solutions to the problems. Then about 10 additional exercises, whose solutions are in a separate manual. Each chapter (made up of the aforementioned sections) ends with an easy test and a hard test.

I like it because it has not too many problems. And each problem is medium to slightly hard difficulty. All of the challenging problems have one or more hints in the back of the book. I also like how they often have you prove important theorems, but they break it down into steps for you to make it relatively easy to figure out yourself.

The problem based approach that it offers could be perfect for some types of learners but bad for others. Overall, I'd recommend it as a workbook that goes beyond the average high school courses treatment of the topic.

Another pic

Thank you for sharing!

hi I'm the user who brought the subject up, not the one with the above pics but here I'll share 1-2 pics of the e-book version of interm algebra. By the way the e-book system they have has insanely good navigation but yeah the biggest problem is you can't find free PDFs

And ofc I forgot pic

...

alright that's enough shilling I guess, on their website they have free excerpts if you're interested

This, king Leo is the man. No one else helps develop intuition like him

Check out this ultimate step-by-step list of how to learn the basics of university-level mathematics, depending on how deep into math you need to go.

>CATEGORY 0:
Algebra – Israel M. Gelfand
Functions and Graphs – Israel M. Gelfand
The Method of Coordinates – Israel M. Gelfand
Trigonometry – Israel M. Gelfand
Geometry: Book I. Planimetry – A. P. Kiselev
Book II. Stereometry – A. P. Kiselev

>CATEGORY 1:
Pre-Calculus - Carl Stitz & Jeff Zeager
Statistics - David Freedman
How to Think Like a Mathematician - Kevin Houston
How to Prove It - D. J. Velleman

>CATEGORY 2:
Calculus: A Modern Approach - Jeff Knisley & Kevin Shirley
Linear Algebra and Its Applications - David C. Lay
Ordinary Differential Equations – Morris Tenenbaum
Calculus of Several Variables - Serge Lang
Calculus Vol. I & II - Tom M. Apostol

>Category 3:
An Introduction to Formal Logic - Peter Smith
Introduction to Gödel's Theorems - Peter Smith
Concrete Mathematics - R. Graham, D. E. Knuth, & Oren Patashnik
Introduction to Probability - D. P. Bertsekas & J. N. Tsitsiklis

>Category 4:
Linear Algebra - K. M. Hoffman & Ray Kunze
Introduction to Partial Differential Equations with Applications - E. C. Zachmanoglou & D. W. Thoe
Fourier Series - G. P. Tolstov
Nonlinear Dynamics and Chaos - S. H. Strogatz

>CATEGORY 5:
Analysis I & II - Terrance Tao
Calculus on Manifolds - Michael Spivak
Visual Complex Analysis" - Tristan Needham
A Book of Abstract Algebra - C. C. Pinter

Dunno any good basic topology books, but I'd put them somewhere in either cat 4 or cat 5. Recommend one please.

>Calculus: A Modern Approach - Jeff Knisley & Kevin Shirley
>Calculus of Several Variables - Serge Lang
>Calculus Vol. I & II - Tom M. Apostol

For what reason? Do one set or the other.

>A Book of Abstract Algebra - C. C. Pinter

That's a book for brainlets.