I need advice on preparations for studying calculus

[user10921]

Hello, I am new to physicsforums and I am still a high school student so I would like to have advice on what books should be relevant on preparation for calculus and more math beyond. I have basic algebra and geometry foundation and I would like to learn more high school math and up. So my plan is Algebra by Gelfand in conjunction with Geometry by Lang/Morrow and How To Prove It by Daniel J Velleman( I have already began this and I'm having quite a little bit of trouble and I think I should postpone this to another time still undecided if you could give me advice I would appreciate), then after I finish those books which would take a while, I go onto Basic Mathematics by Serge Lang in conjunction with Gelfand's trigonometry. This seems a lot in my opinion, so I was thinking I can just do Algebra by Gelfand with Geometry by Lang then move onto Basic Mathematics by Serge Lang. Please give me some good advice because I am not sure on which to do, and if you could critique some of my books it would be helpful as well. Thank you

 

[fresh_42]

Hello and !

Well, your list of books reads quite ambitious for a newcomer, but the books are certainly good choices.

If you have trouble at certain points, you could use our homework forums (please read the rules in this regard, own effort and so), and asks us. If you did this on some occasions, you can still decide whether to postpone a subject or continue either with our help or possibly without, if you learned how to read it. I wouldn't jump too often between the books. It is probably better to learn how to read them than to switch whenever things get complicated. For this an introduction in one specific area which isn't too thick would be best. Maybe you don't chose geometry since this is difficult to communicate via internet, which makes it more difficult to help you.

If you start with linear algebra then you can't go wrong. It is a subject many, many others rely on: mathematics as well as any other scientific field: from physics to economy.

Which book is best for you depends on where you are at and how you understand things best. Give us a chance to know you better (homework) before we recommend a book. Btw., it is called homework section, but it also means help while reading a textbook.

 

[user10921]

Thank you. I believe I am deciding to go through the order of those books since I have about 11 months to completely understand and become more proficient in math.

 

[fresh_42]

Thank you. I believe I am deciding to go through the order of those books since I have about 11 months to completely understand and become more proficient in math.

Anyway, but in case you stuck somewhere, do not lose too much time on single questions. Ask! We will try to help you. Since our rules forbid full answers, this will be a real tutoring. Reading only answers might help in the moment, but it gets you nowhere: easy come easy go.

 

[MidgetDwarf]

Hello, I am new to physicsforums and I am still a high school student so I would like to have advice on what books should be relevant on preparation for calculus and more math beyond. I have basic algebra and geometry foundation and I would like to learn more high school math and up. So my plan is Algebra by Gelfand in conjunction with Geometry by Lang/Morrow and How To Prove It by Daniel J Velleman( I have already began this and I'm having quite a little bit of trouble and I think I should postpone this to another time still undecided if you could give me advice I would appreciate), then after I finish those books which would take a while, I go onto Basic Mathematics by Serge Lang in conjunction with Gelfand's trigonometry. This seems a lot in my opinion, so I was thinking I can just do Algebra by Gelfand with Geometry by Lang then move onto Basic Mathematics by Serge Lang. Please give me some good advice because I am not sure on which to do, and if you could critique some of my books it would be helpful as well. Thank you

If you want a geometry book that is very thorough in its explanations get Moise: Geometry. Do not get elementary geometry from an advance standpoint from the same author. The latter book is far more advanced.

The Serge Lang: Basic Mathematics is solid. I would also buy an old edition of any intermediate algebra book for problems. Don't spend more than 10 dollars shipped.

I didn't really like the Velleman book, but many people like it. Look at either Hammock: Book of Proofs or Levin: Discrete Mathematics An Open Introduction. Both books can be found legally for free online, or you can buy a cheap copy. Answers are in the back of each book. I used both at the same time. I found Levin to be easier to read and introduces you to some very cool math. I like that sections began with a problem that is unsolvable till you read the pertaining section. Which allows you to see and practiced what you learned in said section.

 

[user10921]

Thank you for your advice fresh_42, I will indeed come here if I am stuck on problems or have any questions.

 

[user10921]

If you want a geometry book that is very thorough in its explanations get Moise: Geometry. Do not get elementary geometry from an advance standpoint from the same author. The latter book is far more advanced.

The Serge Lang: Basic Mathematics is solid. I would also buy an old edition of any intermediate algebra book for problems. Don't spend more than 10 dollars shipped.

I didn't really like the Velleman book, but many people like it. Look at either Hammock: Book of Proofs or Levin: Discrete Mathematics An Open Introduction. Both books can be found legally for free online, or you can buy a cheap copy. Answers are in the back of each book. I used both at the same time. I found Levin to be easier to read and introduces you to some very cool math. I like that sections began with a problem that is unsolvable till you read the pertaining section. Which allows you to see and practiced what you learned in said section.

Thank you for taking the time to respond. I have heard very good reviews about Moise's Geometry and I will indeed be keen on getting it. Serge Lang Basic Mathematics is also very good as well I will use it in my 11 month plan. I am liking Velleman's book so far but there are some parts that confuse me like the way he presents certain logical connectives and such.
Also, is Levin's book great for learning discrete math? Does it teach you all the discrete mathematics you must know?

 

[MidgetDwarf]

I majored in Mathematics and do not know what Discrete Mathematics lol. I see it as a hodgepodge of math branches.

It’s very user friendly, and problems are interesting. Really breaks topics down.
Hammock is more formal.It shows the basics of graph theory, combinatorics, modern algebra. But does not go into detail much.

It’s more of. Learning to think in a axiom/definition/lemma/theorem form. Then, “this all the cool stuff you can learn now since you know the ideas of mathematical precision.”

Both books are free so spend an hour or two looking through each of them.

 

[user10921]

Ah I see, thank you for your response. One ladt question though, how did you learn precalculus? What books did you use?

 

[fresh_42]

If Computer Science is a possible goal, then discrete mathematics is certainly a good choice. You do not start encryptions with ERH, but with Euler's $\varphi$ function.

 

[user10921]

I am looking into getting a degree in math, but thank you for your suggestion. As I asked the same question to Midget_Dwarf, how did you learn precalculus, fresh_42? What books did you utilize?

 

[MidgetDwarf]

Ah I see, thank you for your response. One ladt question though, how did you learn precalculus? What books did you use?

I used a combination of Lang and a book called Pre-Calculus: A Problem Solving Approach.

 

[user10921]

I used a combination of Lang and a book called Pre-Calculus: A Problem Solving Approach.

Sorry I lied, a few more questions. What advice do you have for Lang's book? Also, how helpful was it and how long did ittake you?

 

[fresh_42]

As I asked the same question to Midget_Dwarf, how did you learn precalculus, fresh_42?

I'm not sure what pre-calculus is. I assume I learned it at school.

 

[user10921]

I'm not sure what pre-calculus is. I assume I learned it at school.

Ah, my bad. It focuses on elementary functions such as exponentials and logarithms, trigonmetry, analytical geometry, etc. It's usually taught in the US here

 

[fresh_42]

Sorry I lied, a few more questions. What advice do you have for Lang's book? Also, how helpful was it and how long did ittake you?

Lang has probably a very schematic and axiomatic approach. I wouldn't expect too many explanations. If he wrote it as part of Bourbaki, it is more like a lexicon.

 

[fresh_42]

Ah, my bad. It focuses on elementary functions such as exponentials and logarithms, trigonmetry, analytical geometry, etc. It's usually taught in the US here

Yes, that was school math. We have a different system here and I had nine years in high school. Afterwards we directly start at a university.

 

[user10921]

Did you use specific books in your curriculum? And I haven't read any of Lang's books so I hope I adapt to that

 

[fresh_42]

Not at school, i.e. standard school books. Nothing I would recommend. Afterwards we again had standard books, written in our native language, depending a bit on who held the lectures.

Normally I refer to https://openstax.org/subjects since it is for free, but these cannot compete with Lang.

 

[MidgetDwarf]

Sorry I lied, a few more questions. What advice do you have for Lang's book? Also, how helpful was it and how long did ittake you?

I think I have an answered the questions.

 

[user10921]

Not at school, i.e. standard school books. Nothing I would recommend. Afterwards we again had standard books, written in our native language, depending a bit on who held the lectures.

Normally I refer to https://openstax.org/subjects since it is for free, but these cannot compete with Lang.

The openstax project is very resourceful and excellent, I use it to fill in the gaps of my knowledge

 

[user10921]

I think I have an answered the questions.

Alright, Moise Geometry covers 2D euclidean plane geometry? I might accompany it with Kiselev's books as well, but I'm not sure how I can learn Analytical Geometry.

 

[MidgetDwarf]

Just use Moise. It is thorough enough. I think you are over thinking. Just start learning now.

 

[symbolipoint]

Typical preparation for Calculus 1 is this or something like this sequence of courses:

1. Introductory Algebra or Algebra 1
2. Intermediate Algebra or Algebra 2
3. Basic High School Geometry with proofs
4. Trigonometry or the combination course College Algebra And Trigonometry

Once that is done, student is often ready for Calculus 1.
There can be variations in that listed sequence.

 

[smodak]

If you have done basic algebra and geometry, then first read
Precalculus: An Investigation of Functions by Lipman and/or Precalculus: A Prelude to Calculus by Axler