Best Path to study math & physics

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Discussion Overview

The discussion revolves around the best path to study mathematics and physics, particularly for someone with a basic background in algebra but lacking knowledge in geometry and trigonometry. Participants share their experiences with specific textbooks and seek recommendations for study materials and approaches.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant expresses a desire to understand physics and the necessary mathematics, mentioning they are currently reading introductory materials.
  • Another participant questions the specific goals and desired outcomes of studying physics and mathematics, suggesting a need for clarity on the participant's current level and aspirations.
  • Some participants emphasize the importance of foundational knowledge in algebra and trigonometry before tackling calculus and physics, suggesting that these subjects are essential for comprehension.
  • Several participants discuss the rigor of different calculus textbooks, with some recommending "Principles of Mathematical Analysis" by Walter Rudin while others caution that it may not be suitable for self-study.
  • One participant suggests "Calculus" by Spivak as a more accessible rigorous text for beginners, highlighting its intuitive approach and comprehensive exercises.
  • Another participant shares their positive experience with a specific textbook, noting its organization and balance between detail and pace, while also discussing its effective treatment of limits.
  • There are discussions about the availability of resources in different languages, with one participant indicating a preference for starting with English texts before transitioning to more advanced Italian materials.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best textbooks or study paths, with multiple competing views on the appropriateness of various resources and the foundational knowledge required for studying calculus and physics.

Contextual Notes

Some participants express uncertainty about the suitability of certain textbooks for self-study, and there is a recognition that different learners may have varying levels of mathematical maturity and background knowledge.

jedimath
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Ho. Which is the best Path to study math & physics? I have Larson Calculus and Halliday Fundamentals of physics. I have know some algebra. No geometry and trigonometry :(

Thanks.
 
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jedimath said:
Ho. Which is the best Path to study math & physics? I have Larson Calculus and Halliday Fundamentals of physics. I have know some algebra. No geometry and trigonometry :(

Thanks.
Could you tell where you are currently and where you want to end up, since I do not know the specific books?
 
My goal is to understand Physics and study math needed to it. For now I read some pages to see arguments of the book.
 
jedimath said:
My goal is to understand Physics and study math needed to it.
Galileo and Newton, Maxwell, Noether, Schrödinger or Einstein? If your answer is "all", my next question will be "At which university?"
 
Actually I'm a self-taught person. I'm just a simple fan. For work I do something else. For now it would be enough for me to understand all that are topics of the halliday book. A tipic course of General Physics. :)

Sorry for my english. I use google translate.
 
May I ask about your native language? It is probably better to search for appropriate books in that language.
 
Yes, I'm Italian. The books in Italian that I have are a little more advanced than those in English. So, for a first approach, I wanted to start with those indicated (or others recommended by you) and then continue with those in Italian. It is also true that from a certain level on, English books are also suggested in Italy :)
 
jedimath said:
Ho. Which is the best Path to study math & physics? I have Larson Calculus and Halliday Fundamentals of physics. I have know some algebra. No geometry and trigonometry :(

Thanks.
They are good books but you really should study "elementary" and "intermediate" Algebra, and Trigonometry in order to adequately handle studying Calculus and Physics.
 
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Well, as I searched for "fisica per tutti pdf" I have found http://personalpages.to.infn.it/~zaninett/libri/fisicabase.pdf
and FISICA PER LA SCUOLA SUPERIORE from Gerardo Troiano
which both don't look bad. And the first link is a free pdf, so you can simply see how far you get.

In any case you should bookmark PF to ask questions when they occur.
 
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  • #10
jedimath said:
I have Larson Calculus and Halliday Fundamentals of physics.
Larson isn't very rigorous, but Halliday (or Halliday & Resnick + another author) is very commonly used in college physics, and has been for many years.
jedimath said:
I have know some algebra. No geometry and trigonometry :(
As already noted, you need to have a strong background in algebra and trigonometry to be able to understand calculus. Some geometry doesn't hurt, either. You won't get far in physics without a solid foundation in calculus.
 
  • #11
Mark44 said:
Larson isn't very rigorous, but Halliday (or Halliday & Resnick + another author) is very commonly used in college physics, and has been for many years.

What Is a rigorous Calculus book? And for algebra Thanks
 
  • #12
jedimath said:
What Is a rigorous Calculus book?
Principles of Mathematical Analysis, AKA "Baby Rudin," by Walter Rudin is widely regarded.
jedimath said:
And for algebra
Don't know. One algebra textbook is probably as good as another.
 
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  • #13
Mark44 said:
Principles of Mathematical Analysis, AKA "Baby Rudin," by Walter Rudin is widely regarded.

Can I ask you if you read this book?
 
  • #14
Math_QED said:
Can I ask you if you read this book?
No, I haven't.
 
  • #15
Mark44 said:
No, I haven't.

I thought so. If you had you wouldn't have mentioned it. While you are right that it is widely regarded, it is not because it is a good book. It becomes a good book when you are mathematical mature enough. The book is terrible for self-study (really one of the worst books to self-study from if you are new to the material, I tried this some years ago and did not get much out of it). Moreover, the book dives directly into metric spaces and metric space topology which is way too advanced for what the OP needs.

I would recommend the OP the book Spivak's book "Calculus". This is a rigorous math textbook and the author really tries to guide you through the mathematical concepts. There is also a lot of intuition in the book and enough exercises, both computational and theoretical, to really master the material. Whatever your purposes are, either in physics or mathematics, most of the basic material you encounter in this book is essential for going further.

If you have some mathematical maturity, you can also look in the book "The real numbers and real analysis" by E. Block. I read parts out of it, and I especially liked the chapters about the derivative and integral which go further than most texts on these topics do.
 
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  • #17
PeroK said:
This is the one I've got.

https://www.springer.com/gp/book/9781461462705

Bought in Blackwell's bookshop in Edinburgh in 1982!

I'm not familiar with the text but heard good things about it. Mind elaborating why you recommend this text?
 
  • #18
Math_QED said:
I'm not familiar with the text but heard good things about it. Mind elaborating why you recommend this text?

It's got a bright yellow cover.

I think he strikes the right balance between being pedantic about details and not getting bogged down.

It goes at the right pace and has problems from the very easy (assuming you understood the material) to the challenging.

It's well-organised and a good reference.

Specifically, I like the "sequence" formulation of limits.
 
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  • #19
PeroK said:
It's got a bright yellow cover.

I think he strikes the right balance between being pedantic about details and not getting bogged down.

It goes at the right pace and has problems from the very easy (assuming you understood the material) to the challenging.

It's well-organised and a good reference.

Specifically, I like the "sequence" formulation of limits.

Yes, I don't understand why not more textbooks tell something about the connection between limits of sequences and limits of functions. The sequence characterisation of limits makes it often very easy to show that a limit of a function does not exist, while the alternative is an ##\epsilon-\delta##-argument...
 

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