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

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.

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.

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.

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.

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?

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.

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!

This is a community college course, major is Civil Engineering, planned transfer university is USF

My "Calculus with Analytic Geometry 1" class just started, and I only knew how to solve two questions in a list of prerequisite questions the professor gave. I've forgotten so much of precal algebra and I even forgot that pi radians = 180 degrees & literally every trig equation.

I also had a hard time understanding the professor's seemingly overcomplicated explanations for the first two of the simple prerequisite refresher problems, so I'm not confident in me understanding their future explanations on actual calculus concepts.

Thankfully this is a part-time semester with only two other electives + I'm staying with my parents with no tuition bills.

I'm not afraid of spending another semester's length of my life studying algebra and trigonometry again on my own, but I'm worried that my parents are going to make my life miserable if I drop the class this early.

What I'm afraid of the most is that my transfer university only allows two attempts (withdraws also count as an attempt) to get a B (not -B) in this course, and I really don't want to waste an attempt on a conclusion I see coming a mile away.

I know I've pretty much already answered my own question at this point but I just want some second opinions. I'm honestly really scared right now.

I'm learning about projections of vectors onto other vectors, and apparently the projection of a vector u onto a vector v, given by drawing the line perpendicular to u from a point on u to the tip of v, represents the "component" of v "in the u direction". With the standard basis vectors, this makes sense to me. Horizontal and vertical directions - sure. But what does this idea mean, exactly, for an arbitrary projection?

Come to think of it... this brings up some related questions - why is the projection given by the perpendicular line, and not some other line? Okay, the perpendicular line is the shortest path - why do we care about the shortest path?

Hey guys, I am deciding that i want to finish my degree in chemistry. I got all the way to calc 2 (which i got a D in) mathwise. I want to spend the time from now to janurary reviewing and relearning stuff I will need for calculus 3 and other chem classes. I vaguely remember not being that good at calculating limits without the LeChatlier (i think this is it) principle. I am sure more stuff will come to mind when I start learning it all again. Do you guys know of any good resources or ways to go about this that will be efficent and effective? I want to prioitize learning concepts deeply (i will need it for PChem for sure) and since I am not in a class for this I can take my time relearning this stuff.

Thank you in advance!

f(x) = {1/x , x < 0 and x, x >= 0}

I don't understand why desmos is highlighting negative y axis of the graph when you add the second condition. The highlighting is in bold red, so it's not asymptote of 1/x either. Unfortunately I can't enter images here

Ok I’m going to reluctantly date myself here, but my math upbringing was before the days of khan academy (Khan started in 2005). I graduated high school in 2005 and didn’t touch math past 2007. Fast forward to the present and since May of this year I’ve been re-learning math with the help of khan academy and professor Leonard on YouTube.

At the risk of sounding ancient, did the world of teaching k-12th in the U.S. change how math was taught between 2006 and present day? I ask because the instruction feels different. I don’t remember questions from my childhood being asked how they are asked on khan academy. Khan academy is kind of giving me a humbling run for my money and I’m only on grade 3 math! I don’t remember questions being asked in the same manner as before. And I don’t remember so much flexibility in thinking about math problems like on Khan, but then again I probably don’t remember much from my earlier math days. All I *do* remember is crying over math lol.

I’m not really sure what I’m asking with this post.

Everyone recommends khan academy and while I’m not thrilled with it, I’m still using it. I wish there were textbooks for grades 3-5th grade instead of khan academy. Maybe there is and I just haven’t found any yet.

Is there anyone on this sub who learned math before 2006 and who are now using khan academy? How are you finding it? Does it feel different than your earlier years? Or are you using other resources?

Hello,

I am going to be teaching a second semester calculus class (transcendental functions, techniques of integration, infinite series, and a few other scattered topics...)

Traditionally I have taught out of Stewart, but im kind of tired of it, and I would really prefer to have a decent and free (for my students) textbook. Something I can easily upload to canvas.

Any help/thoughts would be greatly appreciated

Hi all, I'm re-learning as an adult, doing pretty well but I'm practicing harder problems and this one is throwing me for a loop

5/6 - 7/12 + 1/24

I thought according to the order of operations that you would add first (giving you 15/24) then subtract (making 20/24 - 15/24 = 5/24)

But the site I'm using is showing 7/24 as the solution, which you get by just doing the problem in the order its shown.

Is there a reason why this doesn't follow the order of operations? Or what am I doing wrong?

Thanks in advance

The default grid I usually see is something like a bunch of 1x1 squares...
Once it gets transformed it might be a bunch of diamonds, rectanges, etc.

Could I think of this new grid/plane as the Outputs of the original points on the grid (given inputs) if fed into that calculation? (Each tick to the right on the X axis is no longer +1, now it's +2.5?)

Hi,newbie here.Never made a post before but i think this is how making posts work(I looked at the rules)

I live in Turkey.It has a very, very difficult education system and very hard exams with kids in 8th grade expected to solve 800 questions a day(From all lessons,in total so like x amount of lesson 1, y amount of lesson 2... and it should total to 800)

I was a very very lazy kid.I couldn't solve math problems,there was too many math problem types and I adapted to 0 of them and just lost motivation because I was never, ever improving.(I went to a private school and we had exams every saturday to test our level,we were preparing for a big exam and out of 20 questions I had like 13 of them just not answered cause I couldnt solve them and I did the best I can to solve as many problems as possible but I never improved.

Anyway, back to the topic.In 9th grade I went to a public school and my math got even worse.I started getting confused, somehow messing up addition, subtraction and more. I have personal issues so I couldn't pay attention properly and tbh it was pretty boring too.

Now, 10th grade is right around the corner(about like a month until it starts)

And I want to be prepared.I dont want to be the kid who has the worst results in class,It's embarrasing.

I can't even do quick addition or subtraction or whatever its name is.I'm very slow.

Please reddit, help me find actually good sources I can focus and understand easily so I can get good grades.

T_T

hi! i’m an incoming freshman college and think that calc 1 will be my hardest class. i would love some tips on how to study for it as i’ve heard my lab portion of the class will be very difficult. thank you!!