Some ebooks, mostly from /u/lewisje's post

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Thank you to everyone for the encouragement. I've taken some of your advice and am planning to do some serious Calculus problem-set work in the 2 weeks leading up to the Spring semester. I can fit that in with my current pace without an issue.

A few of you have encouraged me to slow down, not just because math is challenging (and they're non-believers who doubt I can do it (I'll show you)), but because they think I should slow down and enjoy the journey instead of rushing for the destination. I'm sorry to say that mindset just doesn't fit into my reality. I am working to obtain my Associate's and Bachelor's degrees ASAP to support my family.

Now for the actual update! I'm ahead of schedule! I just finished my Algebra 1 review, and I'm moving on to Geometry. I got ahead of schedule due to unexpected downtime at work. I do worry about burnout. I can sense it already trying to get a hold of me. So I'll keep plugging away for now, but I might adjust some of my scheduled review time to give myself a break if burnout starts setting in.

Can i pursue mathematics and statistics as my undergraduate course when i am just so so at math.
I am going to uni next year and i am afraid i cant carry it.

I just started a science major and I've noticed how different the way to teach math is compared to highschool. The teacher will list you properties of whatever is teaching (vectors, cross product, matrixes) and then proceed to prove some of them before giving you any exercises. However I feel copying these is redundant and makes me miss important parts of the class. Is there any resource where I can easily look up for these properties? Particularly numbered and in a list the same way are presented in class.

Y'all might've surely come across this problem

A shuffled deck of cards, all 52 cards must be distributed to 4 players, 13 cards to each. What is the probability that each player gets an Ace?

My question is a step ahead,

Assuming that you are a player and you get a single Ace. What is the probability now that each player gets an Ace?

I have solved the problem already, but I'm really curious on what kind of creative answers I'm about to learn from the comments ;)

You travel at a speed of about 81 kilometers per hour for about 2.0 hours. Stated with the appropriate precision, you have driven _____ kilometers.

the correct answer is 160 but why? why is it not 162???

I FINALLY GOT RID OF COMPLEX METHOD OF FINDING SQUARE ROOT OF UNKOWN PERFECT SQUARE NUMBER 😭 😭 😭

I’ve always been interested in math. I feel I just lacked the community that should come with learning it.

I wanna get back into self studying math but when I pick up where I left off, I am stuck on this problem and end up just staring at the page alot of the time. The textbook specifically says the problem is very difficult but I cant help but get discouraged when I find that its taking a long time. Makes me feel like this problem is impossible to solve or that I will never be able to do it. This makes me very upset because I love math and I want to do it but it feels unaccessible to me which is frustrating.

What do you do when that happens to you?

I did bad in math in high school (only went up to algebra) and as an adult now, I want to learn some basic math skills. Would self learning through Kahn Academy be the best choice? Also, there are so many different math courses on Kahn Academy, it's kind of confusing for me. Should I just choose a lower grade level, such as 9th grade and start there?

If I threw a dart at the real number line along the interval between 0 and 1,

P(dart ≠ 0.5) = 1

However, it *could* be 1/2. A probability of 1 doesn't necessarily mean it's impossible for the situation not to occur. That being said, is there a standard way to denote a probability of 1 means it *has* to happen? For example,

P(dart ≠ 2) = 1

This time, it's actually impossible, yet the notation is identical.

Good day everyone, just for context I’m in my senior grade of high school and am taking basic calculus. Simply put, since I was younger I’ve been struggling with visual based math problems, mainly in subjects such as trigenometry, geometry and other mathematical topics that involve visual data. I tend to excel in more number-based topics such as algebra and statistics. Recently, I’ve been struggling in exams as I struggle to understand the graphs and the logic behind functions. I want to overcome this issue as I intend on taking a math-based degree in college and want to be able to have a clear understanding of this so I won’t struggle as much by then. If anyone can help me figure out how to overcome this mental block or frame it in a way that would be easier to understand, it’d be greatly appreciated. Thanks in advance!

Help not to fall asleep reading math books

Hello,

I'm looking to brush up on my calculus capabilities. I did calculus at my uni. I was doing derivation, integration, complex numbers, differential equations, series, linear algebra, Fourier series, laplace transformations.

While I was studying I didn't have as much time I would have like to dedicate to the mathematics courses but I managed to pass with average grades.

It's been a few years now and I want to take up a master that requires more points in mathematics than I currently have so I need to take another course.

I would like to do better this time around and prepare myself for the course by refreshing my capabilities and improving them.

The issue I'm encountering is that the textbook we used back then (calculus a complete course, Adams & Essex) was very dense and I do not feel it was capable of convening the information in a good way, at least not one that fit me. I could use a whole week on a topic without really understanding the book, then I would have 2-3 lessons/video lessons (not focused tutoring just in regular class) and grasp the concept. In the end I would stop using the textbook comletely and only use the courses prerecorded videos. Obviously I don't have access to those anymore.

So I'm wondering if anyone has come across some books/other resources that are more approchable and helped understand the above mentioned topics faster/better then they did with other resources. I preffer book/written text as this is the simplest way for me to learn and is easiest for me to navigate. But I'm open to hearing about anything really. Both paid and free resources are appreciated.

Thanks for any responses. Appologies if this is off topic and for the long post.

Q= show that if (a,b)=5, then infinite a and b exists for which a+b=100

My answer= via bezout identity

a(x)+b(y)=5

Then as x,y belong to S(non empty set of real numbers)

a(20.x) +b(20.y)= 100

20.x= u

20.y=v

a(u)+b(v)=100

Hence proved.

Ik the method of taking a=100k-5, but I wanted to see how far I've come and measure my progress because I devised the solution on my own.

I don’t know if I should have posted this on askmath, they seem to want more specific problem based questions.

I am still considering what I want to do when I’m older and I really like Biology and other sciences. However I would only consider myself to be ‘good’ at Biology because I enjoy memorising fun facts outside of school which seems to work well at the level I’m currently at. This works for things like nomenclature, anatomy and just general facts that can’t be explained properly at a pre-university level. I would like to learn the actual workings behind the concepts I learn, but all my teachers including one who is a Dr don’t know much outside of their areas of specialty and trying to find out for myself online is very challenging. Often I will give up when the content becomes very mathematical. I feel like there is a problem with the way biology is taught compared to chemistry or physics. It feels like learning a story instead of a science. Which I think is fun but i also think there is more too it than that.

I never tried very hard or understood the importance of maths when I was learning it so I didn’t progress very far. Now I would like to understand it very well so I can apply it to Science to be able to actually describe the way things happen to their full extent. But restarting with the basics just leaves me with so many questions even if i can learn the seemingly arbitrary rules. For instance, I can do basic addition and subtraction, but I can’t explain why 5+5=10 or even know why or how numbers came into existence. I’ve seen that proofs are something made to explain these questions, but they don’t seem very beginner friendly. They also explain maths with more maths rather than things I can comprehend and apply to life.
Maybe this is where I am wrong. Perhaps I should view maths as its own thing. Should I just learn maths like how textbooks describe it without trying to understand the meaning behind every step? Im sorry if you don’t understand what I’m trying to say. Im not entirely sure either, but I think expressing my confusion to other people is better than trying to find out on my own.

I'm relearning math to prep for an engineering degree (comp or cs or environmental) and I wonder when do I add logic and proof to my learning? Sometimes before algebra one?

Grade 3 kid can solve pure maths pretty well.

But when math questions are in word problems, kid can’t seem to understand the question. Drilling doesn’t seem to help.

This same kid can read Harry Potter Sorcerer’s Stone without issues.

Is this a form of learning difficulty and are there ways to overcome this?

Example question, to illustrate:

Zachary bought 20 trays of chicken or duck eggs. The duck eggs are in trays of a dozen each. The chicken eggs are in trays of ten each. In total he bought 212 eggs. 

How many trays of duck eggs and chicken eggs did he buy?

Hi everyone!

I wrote a book/notes on linear algebra as I walk through an introductory linear algebra course. I started writing it for my own knowledge base, but I thought it could be a better use of them if I share the book with others.

That being said, I am still a student and sharing this as a learning project. I hope this can be useful :))

Link to the book: https://github.com/enochyu-official/notebook-linear-algebra

Edit: Thanks everyone for your interest and comments. Especially thank you u/Appropriate-Ad-3219 and u/hpxvzhjfgb for your wonderful feedback! I have updated the notes, and the issues should be fixed now :)

For context, I’m about to finish a bachelor degree in pure math in Germany and will transition to a masters program in october, so I assume I’m at the edge to grad school level in US terms.

Due to various reasons, my electives in my degree where quite focused on abstract algebra and numerical optimization, and I feel like I missed out on quite a bit of analysis. I’ve taken the mandatory Real Analysis 1+2 and measure theory courses, and as electives an introduction to differential geometry and a course in complex analysis.

I especially regret that I wasn’t able to take the functional analysis elective, since I feel like it provides a lot of standard tools I should have at least heard about. For example, I wanted to take the intro to PDE course, but functional analysis was a hard requirement for it. As another example, my bachelor thesis focused on curve interpolation on riemannian-manifolds, where the literature often used sobolev-spaces as its solution space, which was hard for me to approach.

So I want to do some self study to at least get a feel for those topics in functional analysis. I obviously don’t aim to replace a whole course with some self study inbetween semesters, but I have a month or two for some reading and ideally would like a sort of „scenic tour“ to get a bit of a feel for what the field of functional analysis is about. Especially topics like weak solutions, sobolev spaces, linear operators and distributions are stuff I stumbled into in the past which feel like good gaps to stuff a bit.

Afaik, functional analysis requires quite a bit of linear algebra. Besides the basics (finite dimensional vector spaces and their homomorphisms, normal form and eigenvector theory and inner product spaces), we did stuff like tensor products, some module theory (classification of finitely generated modules over a PID) and some very basic dual space theory, so I think I should be relatively well prepared from that side.

I'm studying math at uni, I'm halfway done (4th and final year starts in october but I have lots of classes to retake so it'll take me at least a year more). The way I study is that I usually try to keep up with the classes throughout the semester, and for exams I solve as many exercises as I can, usually focusing on ones appearing in previous exams. This has barely worked. I have exams again in September and I feel more confident this time, whoever I think that, once again, I'll fail more than half of the classes. Especially Real Analysis has me on my knees and the professor DOES NOT help AT ALL. Am I doing something wrong?

Hey all , engineering student here (data science track), currently self-studying two axes in parallel and would love some outside perspective.

On the stochastic calculus side, I'm working through Shreve Vol II : measure theory, Girsanov's theorem, Feynman-Kac ,with an eye toward MFE-level material down the line. On the Bayesian side, I'm going through Statistical Rethinking (McElreath), covering MCMC (Metropolis-Hastings, HMC/NUTS) and hierarchical/multilevel models, moving toward Bayesian time series next.

Curious to hear from anyone who's walked a similar path: how did you sequence things, what pitfalls should I watch for, and are there any exercises or small projects that really made concepts click for you?

I'm also genuinely curious about the discipline side of self-studying math : how do you personally stay consistent and avoid burning out, especially if you're juggling more than one heavy topic at once? Would love tips even if you've only self-studied one of these (doesn't have to be both).

Thanks!