Where to start, i know, its allready been said, but this is different

Hey, names Tyler, im 17. And due to the fact that I'm lazy in school because all my classes are easy and I dont do my homework. I'm in geometry. I already know everything about geometry though, no joke, got Euclidean geometry (basic geometry right? like planes and stuff like that) licked at high school level. I passed algebra 1 easily. But, I am extremely interested in very high levels of mathematics and physics. For example, I can easily comprehend theory's relating to quantum mechanics. But when I look at the math I have no idea what is going on. So my question draws down and you can see where I am getting with this. I need to start out on what my school calls Algebra 2. I need to learn this so that I can go to pre-cal, then calculus. Then what ever I need to learn after that. But I need a place to start with comprehensive lessons. I tried searching for other links, but nothing that goes down to this simple. I need to almost start from scratch. Please, be patient with me. But please, I want nothing more to do than learn the most advanced math that I can do. Can someone help me please?

What you need is real math that will be expected of you when you enter university. Schools don't teach real math, atleast not public schools, because only 1% of the students will ever need it. What you are learning now is "math applied", which is useful to non-theoretical scientists and engineers. I suggest you get a deeper knowledge of the math you do now and I will suggest to you some books that can help you with that goal.

"Precalculus" by M. Sullivan - this covers all the math you will need to really get into calculus. The level is good. Any eidition is fine, get the cheapest you can buy.

"Numbers: Rational and Irrational" by Niven - this book will teach you basic number theory and also get you used to the way modern math is presented (proofs and theorems). The questions here are excellent, and full solutions are provided in the back.

"Trigonometry" by Gelfand - this book will teach you the elementary theory of trigonometry, and what trig really is. Excellent primer to college level calculus. The only downside is there are no solutions. In math however, this is something you will have to get used to when you enter college, so start now.

To get any real quantum mechanics down, you need a lot of math beyond this and classical mechanics. I would hold it off, as any quantum you do will only be superficial. The books above can be purchased from Amazon.com and are suitable for your level.

Last edited:
Ok, thank you, I will try to find those books. And I wasn't expecting to jump right into quantum mechanics right away, I'm not that naive. I never realized the difference between applied math and theoretical, but I guess that these books will point them out. Thank you again and I'll try to find these books as soon as I can.

Ok, thank you, I will try to find those books. And I wasn't expecting to jump right into quantum mechanics right away, I'm not that naive. I never realized the difference between applied math and theoretical, but I guess that these books will point them out. Thank you again and I'll try to find these books as soon as I can.

Real math is proofs. I was assuming thats what you did in your geometry class. I mean you've seen the words theorem, indirect/contradicion before yes? If not, I suggest getting a proof book too.

The mathematics for qm can be extremely rigorous; for example going into quantum field theory and relativistic qm the math may be more rigorous than phd level mathematics.

However, if you want specifics, for introductory quantum mechanics you are going to need experience in particularly these three areas: linear algebra, partial differential equations, and complex variables/analysis as well as a strong foundation in basic calculus.

Yeah, like I said, I have high school level geometry licked. I just need everything up, so all the basics like things like you said such as linear algebra, partial differential equations, and complex variable/analysis, and strong calculus. I'm going to go look for those books this weekend.

lurflurf
Homework Helper
When you say things like "I have high school level geometry licked.", You give people the impression that you know about proofs and their logic. Linear algebra and calculus can be learned simultaneously. Learn those first then other things. I recomend the books _Linear Algebra_ and _Elementary Real and Complex Analysis_ both by Georgi E. Shilov. If you use a recent standard calculus book you will want a better book to refer to, since every other page will say "for proof see any good book on calculus". You might find it helpful to get a book on introductory applied math.

When you say things like "I have high school level geometry licked.", You give people the impression that you know about proofs and their logic. Linear algebra and calculus can be learned simultaneously. Learn those first then other things. I recomend the books _Linear Algebra_ and _Elementary Real and Complex Analysis_ both by Georgi E. Shilov. If you use a recent standard calculus book you will want a better book to refer to, since every other page will say "for proof see any good book on calculus". You might find it helpful to get a book on introductory applied math.
How can you suggest he begin linear algebra and calculus, even analysis, if he claims not to have even started algebra 2. This means he probably doesn't even know what a logarithm is, or how to graph an inverse.

The mathematics for qm can be extremely rigorous; for example going into quantum field theory and relativistic qm the math may be more rigorous than phd level mathematics.

However, if you want specifics, for introductory quantum mechanics you are going to need experience in particularly these three areas: linear algebra, partial differential equations, and complex variables/analysis as well as a strong foundation in basic calculus.

This advice is more suitable for an undergrad rather than a highschool student. He doesn't even have precalc yet. Don't even touch partial differential equations without ordinary differential equations. In fact, forget the word differential equations exists until you've mastered calculus.

Yeah, like I said, I have high school level geometry licked. I just need everything up, so all the basics like things like you said such as linear algebra, partial differential equations, and complex variable/analysis, and strong calculus. I'm going to go look for those books this weekend.

You have two options. You can go for breadth of mathematics, meaning you can learn the computational side of math the way you are doing in highschool, and probably get through those topics a lot faster and have maybe up to multivariable calculus down before you enter college. This will still enable you to study quantum mechanics, but not deep math. If your sole reason for studying math is to understand physics, then this method works. An example of this is knowing pythogoras' theorem without know its proof.

On the other hand, if you are genuinely interested in math, you can go the depth route. This will be slower, but it will verify all the results and give you a foundation to study advanced math (which is not needed for physics).

As you have not been exposed to real math, it is understandable that you believe you can do both simulatenously with physics the way you can in highschool. Using the latter 2 books I mentioned above will expose you to real math. In any case, you are not ready for any of these topics such as complex variables or pdes. I suggest you use Sullivan to get through precalc, or any other precalc book.

And due to the fact that I'm lazy in school because all my classes are easy and I dont do my homework
Be careful with this attitude. Doing work you don't want to do is important so that you may do the work you want too. There are to many stories of kids who were really bright but never worked hard so when they hit University they just fumbled around after a while. I suggest along with working hard at algebra II and trig, that you do homework, and besides if it is easy, then you should be able to do it quickly.

WarPhalange
On the other hand, if you are genuinely interested in math, you can go the depth route. This will be slower, but it will verify all the results and give you a foundation to study advanced math (which is not needed for physics).

No, but it is helpful so that you avoid pitfalls, such as misapplying a simplification or trick and then bashing your head against the wall for 5 hours before having someone point it out to you.

It also gives you a better foundation for your physics. I have never done a single math proof in my life and I am graduating this year. I just never had to. So when I do physics, a lot of my arguments are "intuitive" by looking at the problem and saying "I can get X from Y, and Y from Z, etc." so often times I can misapply a trick or not see something a math theorem would show that you wouldn't be able to tell otherwise.

lurflurf
Homework Helper
How can you suggest he begin linear algebra and calculus, even analysis, if he claims not to have even started algebra 2. This means he probably doesn't even know what a logarithm is, or how to graph an inverse.
I think the confusion here is more about names that content. Alos the fact that one particular book did things in a certain order does not mean that another order is worse. Algebra 2 is the one that is like "Let R be an entire ring containing a field k as a subring. Suppose that R is a finite dimensional vector space over k under the ring multiplication. Show R is a field.", right? I don't see how that would help with calculus. High school algebra (which does include what a logarithm is, or how to graph an inverse) is helpful for calculus. For linear algebra it is not important to know about logarithms (I supose eventually one may consider the logorithm of an operator, but that is a small worry, linear functions are more important in linear algebra than logarthims) or graphing an inverse. Linear algebra is a good subject to learn early on; it does not logically depend on other subjects, develops mathematical maturity, is an ideal subject to learn to appriciate, understand and invent proofs, and is an important foundation for further study. I find it better to begin with a proper coverage of a topics, then assemple back ground as needed, that may be intimidating for some, but at least in those cases were the proper material is well absorbed time was not wasted. If proper linear algebra is daunting one can begin with sill linear algebra as one find in sinite math books and such. As far as high school level books for review go, the particular book is not important, just avoid bad ones and choose a not bad one that fits you personal style. I like
by Serge Lang
Basic Mathmatics
(learn from the best)
by Mary Dolciani
Pre-Algebra
Modern Algebra: Structure and Method Book One
Modern School Mathematics Geometry
Modern Algebra and Trigonometry: Structure and Method Book 2 Two
Modern Introductory Analysis
(none of these are about what khemix might think they are)
(probably can start on Modern Introductory Analysis it repeats the important stuff from book two anyway like logarithms or graphing an inverse)

by Raymond A. Barnett
Precalculus
Analytic Trigonometry with Applications

by Clement V. Durell And A. Robson
(old fashoned)

As far as what books have analysis or calculus in the title is subjective. Spivak's calculus is harder than many "analysis" books and many "analysis" books are really just calculus books.
This advice is more suitable for an undergrad rather than a highschool student. He doesn't even have precalc yet. Don't even touch partial differential equations without ordinary differential equations. In fact, forget the word differential equations exists until you've mastered calculus.
Terrible ideal differential equations are basic to calculus. You would like calculus students to be unaware that if y=e^e, y'=y ? Though later one studies them on their own. The problem with basic partial differential equations is much background must be assembled. Some ordinary differential equations knowlege is essential and more can be helpful, since ode 1 includes much useless for pde1 and excludes much useful for pde1 such a strong position is suspect.
You have two options. You can go for breadth of mathematics, meaning you can learn the computational side of math the way you are doing in highschool.
Different people learn differently. I think avoiding all proofs is harmful for understanding, everyone should do some. Some people do well learning the proofs as they go. For others the proofs gain meaning once they have an overview of how different parts of the subject relate.

Algebra II in high school has nothing to do with rings. It's just simple solve this quadratic, graph this function, find this inverse, etc.

Hey, names Tyler, im 17. And due to the fact that I'm lazy in school because all my classes are easy and I dont do my homework. I'm in geometry. I already know everything about geometry though, no joke, got Euclidean geometry (basic geometry right? like planes and stuff like that) licked at high school level. I passed algebra 1 easily. But, I am extremely interested in very high levels of mathematics and physics. For example, I can easily comprehend theory's relating to quantum mechanics. But when I look at the math I have no idea what is going on. So my question draws down and you can see where I am getting with this. I need to start out on what my school calls Algebra 2. I need to learn this so that I can go to pre-cal, then calculus. Then what ever I need to learn after that. But I need a place to start with comprehensive lessons. I tried searching for other links, but nothing that goes down to this simple. I need to almost start from scratch. Please, be patient with me. But please, I want nothing more to do than learn the most advanced math that I can do. Can someone help me please?

If you think school is too easy. Try some contest questions, their great on developing interest, problem solving skills and their challenging, so you won't get bored.

You can try AMC 12, if that's too easy then try harder contests.
http://www.unl.edu/amc/e-exams/e6-amc12/amc12.shtml [Broken]

The hardest are http://imo.math.ca/ [Broken]

Last edited by a moderator:
jtbell
Mentor
Algebra 2 is the one that is like "Let R be an entire ring containing a field k as a subring. Suppose that R is a finite dimensional vector space over k under the ring multiplication. Show R is a field.", right?

Not in my high school it wasn't!

Unless high school algebra has really changed a lot in the 40-odd years since I took it... :uhh:

Not in my high school it wasn't!

Unless high school algebra has really changed a lot in the 40-odd years since I took it... :uhh:

That's not high school!!! Haha I don't even understand the question.

mathwonk
Homework Helper
2020 Award
you say you are lazy. thats your main problem. take that as a challenge to overcome. do you think galois and newton were lazy? try to find fascinating topics and, to become consumed with love and interest in your studies. that will cure laziness, plus meeting people more gifted than you. then you may realize you need to work hard to become successful. best wishes. life is long, and wonderful, and you are young and strong.

symbolipoint
Homework Helper
Gold Member
Algebra 2 comments from #11, 12, 14, 15 ----
Do the course names vary depending on country? Algebra 2 = Intermediate Algebra, which is basically a continuation of "Beginning" Algebra. Algebra 2 would typically be linear functions, quadratic functions, more on polynomials and factoring, exponential and logarithmic functions, inverse functions, conic sections (at least a strong introduction), distance formula, systems of equations, sometimes additional topics like sequences and series and binomial theorem.

life is long, and wonderful
lol most pple in my grade are going hating life. I got 2 pple saying how life sucks and stuff in 2 days... like they actully mean it emotionly too.. The only thing keeping me from being miserable is physics. :)

If your 17, shouldn't you be really really busy? I wish I have more time to study just for fun.

Algebra 2 comments from #11, 12, 14, 15 ----
Do the course names vary depending on country? Algebra 2 = Intermediate Algebra, which is basically a continuation of "Beginning" Algebra. Algebra 2 would typically be linear functions, quadratic functions, more on polynomials and factoring, exponential and logarithmic functions, inverse functions, conic sections (at least a strong introduction), distance formula, systems of equations, sometimes additional topics like sequences and series and binomial theorem.

ya I learned all that except Conic sections in school. My teacher just talked about conics for 10min. (Canada)

ya I learned all that except Conic sections in school. My teacher just talked about conics for 10min. (Canada)

my teacher talked about how hard he worked for us so that he can teach us and how corrupt america is when he was supposed to talk about locii and conics for 2 weeks. but atleast he gave us the formulas. (Canada)