- #1

user10921

- 40

- 3

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Other
- Thread starter user10921
- Start date

In summary, the conversation discusses a high school student seeking advice on math preparation for calculus and beyond. They plan on using books such as Algebra by Gelfand, Geometry by Lang/Morrow, How to Prove It by Daniel J Velleman, Basic Mathematics by Serge Lang, and Gelfand's Trigonometry. The advice given is to not switch between books too often and to use the forum for help. A recommendation is also made for Moise's Geometry and an old edition of an intermediate algebra book for practice problems. The person also mentions not liking the Velleman book and suggests looking into other books such as Hammock's Book of Proofs.

- #1

user10921

- 40

- 3

Physics news on Phys.org

- #2

- 19,507

- 25,493

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.

- #3

user10921

- 40

- 3

- #4

- 19,507

- 25,493

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.user10921 said:

- #5

MidgetDwarf

- 1,519

- 666

user10921 said:

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.

- #6

user10921

- 40

- 3

- #7

user10921

- 40

- 3

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.MidgetDwarf said: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.

Also, is Levin's book great for learning discrete math? Does it teach you all the discrete mathematics you must know?

- #8

MidgetDwarf

- 1,519

- 666

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.

- #9

user10921

- 40

- 3

- #10

- 19,507

- 25,493

- #11

user10921

- 40

- 3

- #12

MidgetDwarf

- 1,519

- 666

I used a combination of Lang and a book called Pre-Calculus: A Problem Solving Approach.user10921 said:

- #13

user10921

- 40

- 3

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

- #14

- 19,507

- 25,493

I'm not sure what pre-calculus is. I assume I learned it at school.user10921 said:As I asked the same question to Midget_Dwarf, how did you learn precalculus, fresh_42?

- #15

user10921

- 40

- 3

Ah, my bad. It focuses on elementary functions such as exponentials and logarithms, trigonmetry, analytical geometry, etc. It's usually taught in the US herefresh_42 said:I'm not sure what pre-calculus is. I assume I learned it at school.

- #16

- 19,507

- 25,493

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.user10921 said: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?

- #17

- 19,507

- 25,493

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 said: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

- #18

user10921

- 40

- 3

- #19

- 19,507

- 25,493

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

- #20

MidgetDwarf

- 1,519

- 666

I think I have an answered the questions.user10921 said: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?

- #21

user10921

- 40

- 3

The openstax project is very resourceful and excellent, I use it to fill in the gaps of my knowledgefresh_42 said:

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

- #22

user10921

- 40

- 3

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 said:I think I have an answered the questions.

- #23

MidgetDwarf

- 1,519

- 666

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

- #24

symbolipoint

Homework Helper

Education Advisor

Gold Member

- 7,397

- 1,870

- Introductory Algebra or Algebra 1
- Intermediate Algebra or Algebra 2
- Basic High School Geometry with proofs
- 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.

- #25

smodak

- 459

- 253

Precalculus: An Investigation of Functions by Lipman and/or Precalculus: A Prelude to Calculus by Axler

The essential materials for studying calculus include a textbook, a notebook, a calculator, pencils, and graph paper. It may also be helpful to have access to online resources or a study group.

To prepare for studying calculus, it is important to have a strong foundation in algebra and trigonometry. It may also be helpful to review basic concepts and practice solving problems before starting the course.

The amount of time needed for studying calculus may vary for each individual, but it is generally recommended to dedicate at least 2-3 hours per week for each credit hour of the course. This may increase depending on the difficulty level of the course.

Some helpful study techniques for learning calculus include practicing regularly, breaking down complex problems into smaller steps, and seeking help from a tutor or professor when needed. It may also be beneficial to create study guides or flashcards to review important concepts.

Some common mistakes to avoid while studying calculus include not practicing enough, relying too heavily on a calculator, and not seeking help when struggling with a concept. It is also important to avoid procrastination and to stay organized with notes and assignments.

- Replies
- 4

- Views
- 4K

- Replies
- 38

- Views
- 8K

Foundations
Theoretical Books on Mathematics

- Replies
- 4

- Views
- 2K

- Replies
- 4

- Views
- 2K

- Replies
- 7

- Views
- 3K

- Replies
- 1

- Views
- 2K

- Replies
- 5

- Views
- 2K

Number Theory
Cryptanalysis Books: Prerequisites for Beginners

- Replies
- 9

- Views
- 1K

- Replies
- 3

- Views
- 2K

Intro Physics
Reading plan for self-studying parallel to classes

- Replies
- 15

- Views
- 2K

Share: