Starting from Scratch and learning Advanced Math

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Discussion Overview

The discussion revolves around the process of learning advanced mathematics from a very basic starting point, focusing on the recommended order of topics, resources for self-study, and the motivations behind learning mathematics. Participants share their experiences and suggestions for materials, while also exploring the relationship between mathematics and physics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • One participant expresses a desire to learn mathematics from scratch and seeks a recommended order of topics, emphasizing the need for a structured approach.
  • Another participant suggests starting with calculus and linear algebra as foundational tools, noting that school mathematics often lacks depth in fundamental concepts.
  • There is a discussion about the importance of identifying personal goals in learning mathematics, such as whether it will be used as a tool for physics or pursued as a standalone subject.
  • A participant mentions their uncertainty about specific interests in mathematics and expresses a desire for a general grounding before exploring further.
  • Recommendations for resources include a suggestion to start with a linear algebra textbook and possibly a calculus textbook to gain insight into the subject's breadth.
  • Participants mention online resources, such as Exam Solutions, which cover the UK school mathematics syllabus, as a way to assess current knowledge and starting points.

Areas of Agreement / Disagreement

Participants generally agree on the need for a structured approach to learning mathematics and the importance of identifying personal goals. However, there are multiple competing views on the best starting point and resources, and the discussion remains unresolved regarding a universally accepted order of topics.

Contextual Notes

Some limitations include the lack of consensus on the specific order of topics to learn and the varying motivations among participants, which may influence their recommendations. Additionally, the discussion does not resolve the question of which resources are most effective for self-teaching mathematics.

Who May Find This Useful

This discussion may be useful for individuals interested in self-studying mathematics from a basic level, particularly those who are unsure of where to start or how to structure their learning journey.

Information Overload
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If someone wanted to learn maths to a high level starting basically from scratch (knowing little more than basic addition, subtraction, multiplication and division) which order would you recommend that they learn things in? Is there a generally accepted/recommended order?

I'm interested in learning more about maths but I haven't really done much since school (a long time ago) and I've forgotten most of that. I'm hoping that at least some of it will come back to me as I go along. I have tried a couple of times to learn by myself in the past but, without a plan, I tend to fall off the wagon pretty quickly which is a shame because I really would love to learn more.

Also, can anyone recommend any good materials for self teaching maths? Classes aren't an option for me right now, so I'll have to rely on books or YouTube. I have a couple of math books (things like 'Basic Maths for Dummies') and I'm aware of the Khan Academy but are there any others that are worth a look?
 
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Information Overload said:
If someone wanted to learn maths to a high level starting basically from scratch (knowing little more than basic addition, subtraction, multiplication and division) which order would you recommend that they learn things in? Is there a generally accepted/recommended order?
Of course there is a "natural" order given by the order it is learned at school and then college. Here it starts (after school) with Calculus and Linear Algebra as basic tools. The crucial point is that mathematics at school hasn't a lot to do with mathematics itself. School math is more or less a description of how to do calculations rather than to bother about the fundamental concepts underneath this surface.
I'm interested in learning more about maths but I haven't really done much since school (a long time ago) and I've forgotten most of that. I'm hoping that at least some of it will come back to me as I go along. I have tried a couple of times to learn by myself in the past but, without a plan, I tend to fall off the wagon pretty quickly which is a shame because I really would love to learn more.
In my opinion you should first ask yourself where you intend to end up. Which questions do you want to be answered? Do you want to learn math as a tool for physics, e.g., or as a science of its own? Are there any specifics that drives your motivation? The answer you'll have to these questions are suited to get a better and more specific advise. Plus a better path towards these goals.
Also, can anyone recommend any good materials for self teaching maths? Classes aren't an option for me right now, so I'll have to rely on books or YouTube. I have a couple of math books (things like 'Basic Maths for Dummies') and I'm aware of the Khan Academy but are there any others that are worth a look?
I'll leave this point to more qualified (and native speakers) than me.
 
fresh_42 said:
In my opinion you should first ask yourself where you intend to end up. Which questions do you want to be answered? Do you want to learn math as a tool for physics, e.g., or as a science of its own? Are there any specifics that drives your motivation? The answer you'll have to these questions are suited to get a better and more specific advise. Plus a better path towards these goals.
I haven't really thought that far ahead yet. I don't know enough about maths to say that any particular area interests me. I just want to get a general grounding in the subject and see where it takes me. I am interested in physics as well but I have the same problem there; I just don't know enough to say where I want to go with it, just that I'd like to find out more about what's out there. I also think that having a decent grounding in maths is a good idea before I try tackling physics. One thing at a time and all that. :)

That's probably not very helpful I know, but it's all I have at the moment. I don't see myself ever having a career in a maths or science related field, so I guess you could say that this is going to be a hobby for me but I take my hobbies seriously. I want to go as far as I can go and learn as much as I can learn.
 
Then start with a cheap paperback on linear algebra, e.g. https://www.amazon.com/dp/8184896336/?tag=pfamazon01-20

It will get you an impression on how mathematics is different from the version taught at school and simultaneously contains what will be needed as well in physics as in mathematics. It would be a first step. Alternatively or additionally choose a textbook on calculus I. This way you can also get an impression on how far spread the entire adventure can develop.
 
The UK school maths syllabus is covered online at Exam Solutions, if you Google for that.

It covers both GCSE and the more advanced A levels.
 
PeroK said:
The UK school maths syllabus is covered online at Exam Solutions, if you Google for that.

It covers both GCSE and the more advanced A levels.

Here's the link. It's a worth a look at least to establish what you know and where you are starting from.

http://www.examsolutions.net/
 

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