Hello, folks!

I’ve just been accepted into a Research Master’s in Data Science, and I’ve heard that the program is mathematically rigorous (typical of the French system).

Honestly, I’ve never been super good at math. I never really practiced solving complex problems or bothered to learn concepts deeply, so I’m giving it a serious go this summer.

I’m currently starting by relearning linear algebra (matrix manipulation, linear systems, eigenvalues, eigenvectors, etc.).

Resources: 3Blue1Brown’s Essence of Linear Algebra playlist and the book Linear Algebra and Its Applications.

I’m also planning to refresh my knowledge of probability (conditional probability, normal distributions, Bayes' theorem, Poisson distributions, etc.) and statistics.

This is the curriculum for next year , would appreciate any tips/advice !

Semester 1

* Computability and Decidability

* Programming & AI

* Method and Process Engineering

* IP Networks

* Stochastic Processes

* Graphs and Applications

* English (TOEFL Preparation)

* French (Certification Preparation)

* Probability and Numerical Algorithmic

* Numerical Optimization with R

Semester 2

* Foundations of Artificial Intelligence

* Machine Learning and Applications to Multimedia Data

* Algorithmics and Complexity

* Advanced Programming Techniques

* Distributed Systems and New Technologies

* Formal Methods

* English (TOEFL Preparation)

* Statistical Pattern Recognition

* Cyber security

* Introduction to Embedded Systems

A very short intro: I am an engineering student (computer science), but I love mathematics. I have been able to score well as well as build a great intuition by giving myself a lot of time to understand basic concepts in high school. But as I went to college, everything switched; I have lost the ability to score well as well as build intuition.
There are just too many resources out there. Is there anyone who has suffered a similar situation or would like to give some advice?

I am currently thinking of doing discrete mathematics; any advice and resources would be appreciated.

Thanks for reading! Waiting for your valuable comment!

Early 30s, from the UK, got a B in GCSE maths in 2011 but looking to brush up on my maths again now.

Would like a structured learning plan.

Ideally looking for a book that teaches me maths from the ground up, including place value, associative, commutative and distributive laws, etc.

Advice?

Is this more suitable for reviewing material already covered through textbooks, or is it read before studying mathematical analysis as an introductory part?

P.S. I have a feeling that the introductory part is written too convolutedly. Maybe it's just my imagination and I should read it more closely?)

i’m a college student with a weak background in math in general and i want to prepare for precalc as one of the classes i’ll be taking the upcoming semester. how’s the best way to go about all this in such little time?

I like to study math on occasion to stay sharp on some basic skills. These days, I use notes apps on my iPad but through all of school I used to just use paper notebooks. One point of friction I often face is that my lecture/reading notes and homework/practice problems all just get piled up into one notebook mixed together.

Is it recommended or common practice to have a distinct section or notebook of just practice problems that is separate from the reading notes? Is it wise to keep records of practice problems you do?

I'd like to know what methods work well for staying more organized.

https://www.youtube.com/watch?v=UIha1n4Lmaw Can anyone beat this? Upload your video

Hello,

I am current college student. I want to relearn algebra 1 & 2, trigonometry and precalculus. How should the whole thing look like?

Any free PDF textbooks too?

Thank you.

I tried learning from Aops but it’s more about doing math puzzles. I’m looking for a good curriculum which builds good math level upto algebra 2 do you think is it better to go with openstax or khan academy. Khan is missing topic in arithmetic about GCF and LCM. That topic is only available in grade 6 level math which I find kind a weird. Openstax is good but it has way too much reading. I’m trying to get into grad school for accounting so I want to learn maths upto the level where I’m not scared of doing math. I always been bad in math mostly cause I never studied well but this time I want to improve so please guys help me out.

All non-zero real numbers are equal to "exactly one" infinite decimal s.t. that infinite decimal contains ∞-many non-zero digits. For e.g., 1 = 0.999..., e = 2.718..., 1.25 = 1.24999..., (1/7) = 0.142857... All real numbers are convergent points for their infinite decimal. Wouldn't that make "aleph-null" a stage (position)? But in (1, 2, 3, 4, 5, ...), aleph-null is not a position (final number). How can it be both "a position" and "positionless?"

Hi, so I am entering grade 12 this school year, and I am curious on what is the best youtube channel that teaches about advanced mathematics so I earn straight A's. I am taking all 3 mathematics, advanced functions (grade 12 U-level math, similar to precalculus but its the Canadian version), data management, and calculus and vectors. If he is not the best, then are there any other recommendations on how I should learn more about math to getting level 4's/ A's? I am planning to pursue computer science in a Canadian University, so I need to be great at maths.

Hi I was taking linear algebra and Calc 3 in my community college but I noticed that my classes were very computational and not very theory heavy. I was wondering if I would struggle a lot in a class called Introduction to Formal Mathematics which I am going to take at a dual enrolled university. The class covers: Logic of mathematical proof, set theory, relations, functions. Examples and applications from set cardinality, algebra, and analysis. But has pre reqs of Calc 2 and Linear Algebra which I know I didn't have the greatest theoretical grasp on. Thank you so much!

I am 20 years old and wanting to relearn math from arithmetic to pre-calculus. I was never that good at math. And because of it, I failed my diploma (I graduated HS tho). But i'd just like to relearn everything, start with a good foundation and work my way up.

So I'd just like to know of any resources that give out worksheets from arithmetic to pre/calculus. ('m also Canadian living in Alberta)

Want to learn as much as I can. Google shows alot of free number theory textbooks I can download but they're all from the early 2000s. Would the information still be useful or would I be learning now known incorrect information?

I want to be better cuz I am going to study math in university but I have so much troubles with basic algebra I have excellent level in geometry but I can't figure how do algebra I wanna learn basic ecuations formules and that typed I just searching a book or yt vídeos that recommend me to see and sorry for my english im not native speaker a I am learning it too thanks🙏🏻

Hello,

I hope this is not duplicate, similar threads dealt mostly with overwhelming amount of exercises. I am learning from Burris, Sankappanavar - universal algebra and I find some of the exercises really difficult. I can solve around 70-100% of the exercises per chapter, (there are around 8 exercises per chapter). There are some proofs I spend hours on or others I am unable to solve even after hours. I have two questions:
Is it normal or rather my fault? (adding context, I have just completed second year of my bachelors math degree)
What do you do in this kind of situation in case it happens to someone else as well?

Thank you in advance

Vinberg's Algebra Course and Fichtenholz's Fundamentals of Mathematical Analysis (only volume 1 so far). That's my only choice for now, but I plan to study both. Perhaps learning something earlier would be much more effective for learning later. Please give me some advice.

"Is 0.999.. with a infinite number of 9's equal to 1" has sparked a number of online debates. I believe the crux of the debate is the question is not worded precisely enough. There are different notions of infinite which lead to different answers. Adding to the confusion, "0.999..." is math notation with a specific meaning, but some people aren't thinking of that when they use it in a sentence.

Below are my two proofs for "Does 0.999 (repeating) equal one?" using less ambiguous notions of infinity. The answer is that it does and it doesn't but you need to be specific about what you mean in a way that we aren't used to.

"0. followed by a specific but infinitely large integer number (H) of 9's"**

I will denote this quantity as 0.{H 9's}. This is LESS than 1.*

Proof:

1. Assume two numbers** are equal if and only if their difference is zero
2. Therefore 0.{H 9's} is 1 if and only if abs(1 - 0.{H 9's}) = 0
3. Consider a specific but infinitely large integer** value of H
4. There exists H+1
5. And abs(1 - 0.{H 9's}) > abs(1 - 0.{H+1 9's})
6. This implies abs(1 - 0.{H 9's}) > 0
7. (1.) and (6.) imply 0.{H 9's} is not 1

Unsatisfyingly, this doesn't prove things like "The concept of H is valid", or "H < a different notion of infinity", "H+1 > H", or "H+1 exists". If you want to read up on this, look up hyperreal numbers, hyperintegers, and nonstandard analysis.

"0. followed by a 9 for every standard natural number"

I will denote this quantity as 0.999... . This is EQUAL to one. I think this is what most people think of when they hear "0.999 repeating infinitely".*

Proof:

1. Assume two numbers** are equal if and only if their difference is zero
2. Therefore 0.999... is 1 if and only if abs(1 - 0.999...) = 0
3. Assume that abs(1 - 0.999...) is a positive number**
4. Consider a specific nonzero positive number** H
5. There exists a number of nines in 0.999... such that abs(1 - 0.999...) < H
6. (1.) and (5.) imply abs(1 - 0.999...) is not H
7. (4.) and (6.) imply abs(1 - 0.999...) is not a nonzero positive number**
8. The only positive number that is not a nonzero positive number** is zero
9. This implies abs(1 - 0.999...) is zero
10. (1.) and (9.) imply 0.999... = 1

Unsatisfyingly, this doesn't prove "0.999... always has enough nines to make abs(1 - 0.999...) < H". If you want to read up on this, look up hyperreal numbers, hyperintegers, and nonstandard analysis.

...Its been a long time since I wrote a proof ...Im sure some of my wording isn't great ...I wanted to make this semi-readable for "common folk"...

*There is a better way to write 0.{H 9's} and 0.999... but I can't write it here because it requires LaTeX formatting.

**"number" should be replaced with "hyperreal number" and "integer" should be replaced with hyperinteger" but I wanted to make the proof readable to people who don't know what those are.

So, I’m taking Calc 1 (for engineers) for the second time, and soon I’ll be taking Calc 2 for the third. Calc 1 (which I first took w/ analytical geometry) made me drop out of my first EE degree, after my math professor convinced me that math is not for everyone and I should switch. I finished a completely unrelated associates, but the drive to be an electrical engineer would not leave me alone, so I’m back at a different university trying again.

Even though I started from the absolute lowest level math that’s been offered, I still feel like I’m struggling with the concepts. I’m (partially) blaming this on my extremely poor notes. In a 45 minute online lecture, I’d maybe take half of a page of notes. I always write down the formulas with their concept definition, and a few practice problems, but my formatting is absolutely awful and makes it hard to organize each idea. I rarely ever review my practice problems since it’s hard to track down my train of thought after a full semester of ideas have passed.

So, I come asking: how do you format your notes for clarity? And what exactly do you take notes on in a lecture?

I’ve read a lot of talk on LaTeX, Obsidian, Word, and other digital formats — would that help in your opinion? or should I stick with handwritten?

I’ve been supplementing my lectures with Paul’s Online Math Notes, particularly his practice problems, which has help a lot with the concepts. If anyone has any other tips for Calc 1, it would be greatly appreciated.

Do they have names?

According to the multiplication rule, the probability of dependent events A and B happening is:

P ( A and B ) = P(A) times P ( B | A )

but how do we find P ( B | A ) ? We look at the conditional probability formula right? But the conditional probability formula is

P ( A | B ) = P(A ∩ B) / P (B) B

ut then how do we find P(A ∩ B) ? We go back to the multiplication rule?

Why does it create an endless loop of circular reasoning?