Help relearning mathematics.

In summary, the individual is beginning an undergraduate course in Mathematics (specifically Philosophy and Mathematics) and is seeking guidance for revising. The course will mainly cover Linear Algebra and Calculus, and the individual is asking for tips, good sources for learning, and which subjects they should focus on. They have not specified if they have previously studied Linear Algebra and Calculus and are advised to study the books used in the course and seek coaching on writing clearly. It is suggested to ask for more advice on the Physics Forums > Science Education > Academic Guidance section. Additionally, it is recommended to focus on understanding proofs rather than just calculating and to have a strong foundation in Algebra and Trigonometry.
  • #1
cfgsa
6
0
I am, then, to begin an undergraduate course in Mathematics (Philosophy and Mathematics, precisely) and I am in need of some help.

It's been over two years since I last studied maths in school, and so I would like counsel as to what you consider would be sensible revising. I understand that my course touches mainly on Linear Algebra and Calculus ; what should I be looking at , any particular tips to get me on my feet , good sources for learning and studying alike , which subjects should I peruse ?

Thank you .

C
 
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  • #2
You aren't making it clear whether your are taking one undergraduate course (presumably titled "Mathematics And Philosophy") or whether you are undertaking a course of study, such as double major in Mathematics And Philosophy.
 
  • #3
Stephen Tashi said:
You aren't making it clear whether your are taking one undergraduate course (presumably titled "Mathematics And Philosophy") or whether you are undertaking a course of study, such as double major in Mathematics And Philosophy.

I will be studying an undergraduate course, for a Joint-Honours degree in Philosophy and Mathematics.
 
  • #4
Do you have a specific description of the course? - a syllabus?

I can visualize one type of course that would study the general concepts of mathematics and emphasize the history of mathematics. I can visualize another type of course that would make heavy use of symbolic logic (a topic often taught in the Philosophy department).
 
  • #5
Stephen Tashi said:
Do you have a specific description of the course? - a syllabus?

Introduction to Linear Algebra (using the book 'Linear Algebra, A Modern Introduction' by David Poole):

- Complex Numbers (Appendix C) (3)
- Vectors and geometry (4)
- Systems of linear equations, echelon form, Gaussian elimination, intro to span and linear independence. (6)
- Matrices, multiplication, transpose, inverses, linear maps. Intro to subspaces and bases. Rank. (8)
- Eigenvalues and eigenvectors. Determinants (6)
- Orthogonality, Gram-Schmidt, orthogonal diagonalisation. (5)
- Introduction to abstract vector spaces and subspaces. (4)
- Selected applications (taught in sequence where appropriate) (4)andCalculus and its applications (using 'Calculus' by James Stewart):

1. Understanding of the ideas of limits and continuity and an ability to calculate with them and apply them.
2. Improved facility in algebraic manipulation.
3. Fluency in differentiation.
4. Fluency in integration using standard methods, including the ability to find an appropriate method for a given integral.
5. Facility in applying Calculus to problems including curve-sketching, areas and volumes.
6. Understanding the ideas of infinite series including Taylor approximations.
7. Understanding the ideas of differential equations and facility in solving simple standard examples.
 
  • #6
cfgsa said:
I am, then, to begin an undergraduate course in Mathematics (Philosophy and Mathematics, precisely)

To me, it looks like you're taking Linear Algebra and Calculus. I don't see where the Philosophy comes in. You said you studied mathematics two years ago, but you didn't say if you have previously studied Linear Algebra and Calculus. How long do you have to prepare for this course? (The syllabus could be interpreted as 3 semesters of courses.)
 
  • #7
Stephen Tashi said:
To me, it looks like you're taking Linear Algebra and Calculus. I don't see where the Philosophy comes in. You said you studied mathematics two years ago, but you didn't say if you have previously studied Linear Algebra and Calculus. How long do you have to prepare for this course? (The syllabus could be interpreted as 3 semesters of courses.)

Sorry , I did not give you the details on the Philosophy subjects —which are separate— because I did not need advice for those.

Thanks!
 
Last edited:
  • #8
The topics from philosophy would be relevant if they are taught in the same course. The would not be relevant if taught in a different course.

I suggest you study the books that are to be used in the course. Don't linger over the first chapters. Try to work a few problems from the middle chapters of the book if you have studied the material before (a fact you have not yet revealed). Get some coaching about how to write clearly.

If you want more advice, ask your question again in the forum section:

Physics Forums > Science Education > Academic Guidance

and you'll get more advice than you can follow. Include the results of this cross examination in your post.
 
  • #9
Stephen Tashi said:
If you want more advice, ask your question again in the forum section:

Physics Forums > Science Education > Academic Guidance

and you'll get more advice than you can follow. Include the results of this cross examination in your post.
An alternative to this is to use the report button to request that this thread be moved there.

cfgsa said:
It's been over two years since I last studied maths in school, and so I would like counsel as to what you consider would be sensible revising. I understand that my course touches mainly on Linear Algebra and Calculus ; what should I be looking at , any particular tips to get me on my feet , good sources for learning and studying alike , which subjects should I peruse ?
If your goal is to pass the exam, you should ask your professor, not us. If your goal is to understand stuff, I suggest that you spend a lot of time studying proofs of theorems, and less time on how to calculate stuff. In linear algebra, I think one of the most important details is the relationship between linear operators and matrices (post #3 in this thread). I find it very strange that people who show up here after taking a linear algebra class don't know this, or even that the definition of matrix multiplication is [itex](AB)_{ij}=\sum_k A_{ik}B_{kj}[/itex]. In calculus, I find it more rewarding to know the proofs of e.g. the fundamental theorem of calculus, the rules for derivatives (product rule, chain rule, etc.), and the fact that the series that defines the exponential function is convergent, than to know how to do difficult integrals.
 
  • #10
I teach Calculus and I can tell you that you will need a good foundation in Algebra and Trigonometry to succeed in Calculus as most of the problems are only half Calculus. The rest is Math from previous years. Scan the internet and find "cheat sheets" for Algebra and Trig that summarize what you should know and then go to www.purplemath.com to the lesson index and learn what you need to know.

As for Linear Algebra, you need to brush up on vectors and matrices. Check out my website for my Summary Sheets on Vectors and Matrices at www.scribd.com/pfreda. To download you will need a Facebook Acct or signup at scribd.com with an email address.

Good Luck
 
  • #11
Thank you very much for your help ! I am not looking to merely pass the exams but to truly understand.

c
 

1. How can I improve my math skills?

To improve your math skills, it is important to practice regularly and seek help when needed. You can also try different techniques such as breaking down problems into smaller steps, using visual aids, and finding real-life applications for math concepts.

2. What are some effective strategies for relearning mathematics?

Some effective strategies for relearning mathematics include starting with the basics, reviewing fundamental concepts, and practicing regularly. It can also be helpful to work with a tutor or join a study group to receive personalized support and feedback.

3. How long does it take to relearn math?

The time it takes to relearn math varies for each individual. It depends on your current level of understanding and the amount of effort and dedication you put into practicing and studying. With consistent effort and the right strategies, you can make significant progress in a few weeks or months.

4. Are there any online resources for relearning mathematics?

Yes, there are many online resources available for relearning mathematics. Some popular options include Khan Academy, Math is Fun, and Math Planet. These websites offer free lessons, practice problems, and interactive activities to help you improve your math skills.

5. Is it possible to relearn math at any age?

Yes, it is never too late to relearn math. With the right approach and determination, anyone can improve their math skills at any age. It is important to have a positive attitude and believe in your ability to learn and improve.

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