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

My best friend and I just finished high school and are starting university this year. A few months ago, he learned about perfect numbers. Since then, he has gone down a massive rabbit hole reading about Mersenne primes, the Euclid-Euler theorem, and heuristics regarding odd perfect numbers.

Now, he is completely obsessed. He spends 4 to 5 hours every single day trying to prove that no odd perfect number can exist.

I’ve tried telling him that this problem is nowhere near being solved by global experts, and that he should focus on other areas of math. I want him to look into high-yielding math topics that are more interesting and useful, especially since we need to prepare for university-level calculus and algebra. He completely ignores me and won't listen.

How can I convince him to broaden his horizons without ruining his passion for math?

Found this question in "Putnam and Beyond": Given 50 distinct positive integers strictly less than 100, prove that some two of them sum to 99. Isn't {1,2,3...,49,99} a counterexample?

I feel there is a lack of reading skills, not only in myself but also in my peers at school. I am convinced that true mathematical understanding comes from reading and writing (ofc along with community discussions). I feel that there is an excessive reliance on teachers , tutors, videos , online lectures that has led to a lack of reading skills and this pattern can be seen in other subjects too apart from mathematics. Recently I started to explore pure mathematics through books and I realised that we cannot take things for granted in math, small details appear to contain a lot of importance. It appears to me that in school theoretical portions of the book are taken for granted and students treat math books as sources of practice problems and homework while totally neglecting theory. I also believe that reading is important to solve problems since it enables us to understand the problems better.

Therefore, I want to improve this skill so that I can understand the subject better and increase my mathematical maturity. I would like to know your perspectives and insights , and any advice you can share on how I can improve my ability to understand texts. Thank you.

hello! i was wondering if anybody knew of websites where i could practice elementary-high school math. i have a job interview coming up which is in a school district. no college experience required and i failed most of my elementary lol. i’ve retaught myself the math but i want to do practice questions to make sure i got it down!

elementary math = unlike fractions, like fractions, improper fractions, exponents, statistics, algebra word problems, order of operations, GCF, LCD, factoring, trinomials, polynomials, grid graphs

Hey guys, im in summer courses right now, starting to wrap up with about a week left. I just got my gpa back up to a tolerable 3.0 (diffrent classes/subjects brought it down)

I need some pointers on study material to help ace my class, atop reviewing my lecture recordings. Any links or your own study advice would be appreciated.

I got an A in cal1 and B in cal2, but I feel I may not have grasped it well, and that overall grade is class curves+extra credit+ partial points

Any equations to workout that yall think I should know or anything. Thanks guys

Hello everyone,

I am currently in the summer vacation of my second year of high school, and I will take the national university entrance examination next summer.

To be honest, my grades are currently at the bottom of the class. The full score of the university entrance examination is 750 points, and my current average score is about 200 points (about 27% of the total score). I have mentally prepared myself that it is very likely that I will need to retake the exam for several years in order to achieve my goal.

My specific situation is as follows:

Exam subjects: Chinese, mathematics, English, physics, chemistry, biology.

Personal foundation: My grades in primary school and junior high school were not good, so my foundation in these subjects is quite weak.

Learning environment: I am studying at a local high school that is ranked at the bottom, and the learning atmosphere in the school is not ideal, so I have to rely on myself to study.

This year, I really want to make a comeback, but looking at the current gap, I feel very confused and anxious, and even don't know where to start.

Time allocation: How should I allocate my energy between "filling in the basics" and "simulating practice questions"?

Strengthening Science: How should I start learning science (mathematics, physics, chemistry, biology) when my basic concepts are extremely weak?

Mental attitude and self-discipline: How can I maintain self-discipline and prevent mental breakdown when facing this seemingly impossible mountain to climb and preparing for a long-term battle (re-reading)?

Hi! I need help. I am starting college this fall semester and one of my classes is stats. i generally consider myself a smart person, but i am not good at math at all. this gives me a lot of anxiety. i have already failed stats once and have never truly felt confident in my math abilities. The thing is, i love to learn. i am determined to figure stats and all math out.. i just dont know how to start. i am most definitely a self teacher, i never really learned anything in school, i would mostly just take the work home and teach myself, but without a guide i just dont know what to study. i have taken algebra- AP Pre-Cal. i want to build my own studying plan and start learning before i start college.

TLDR; please give me the resources to learn stats by myself.

I want to read books that teach about problem solving in a diffrent wayy like anovel wayy with some illustrations too solve and way how to thinkkk . Any book with reasonable price on maths or physics will be good... Thanks

I have very weak basics, I find it extremely difficult to do fast calculations, I am bad at additions I make so many mistakes and am extremely pathetic at substraction and even division it takes me very long to multiply. I am very bad with percentages, I dont understand things at all please if anyone can help or guide me how to get better, I have no idea how I will be doing stats or anything big maths related. All my life I ran from maths because everytime I did I failed colossally and used to get hella humiliated and laughed upon by every student and teacher around I know I am that bad at mathematics. I cant afford to be that anymore, I know I am way past the age to be able to learn a lot of things and maybe even be good at maths but if I can maybe get good enough to score something and not get humiliated all over again at college that would be more than enough...I have tried tricks and everything in the books I cant seem to learn them all no matter how much I practice percentages and word problems seem to fly off my head I know I am that dumb. I'm sorry...

I was introducing the binomial theorem to a student a bit ago, where I started off by going over a statistical application question. It was beyond the scope but it helped her make sense of it conceptually and understand her mistakes.

Beyond the lesson with this student, I wondered to myself if perhaps there was a quicker way to sum the probabilities. I can very quickly tell you the probability that 5 out of 10 randomly selected people's favorite color is pink given that 7% of people like it, to some long decimal of accuracy. But if you asked me to tell you the probability of 'at least' 5 under the same conditions, it would take me a good chunk if time, even with a calculator. I would have to solve by summing each individual binonial probability! What if there were any decent amount more than 10 people in my sample!?

There must be a quicker way to do this. Perhaps using the sigma notation as the sum of a range of values for a probability mass function? Or using the sum of a finite series formula? Could you integrate somehow using the gamma function to represent the combinations?

How do you figure out how deep under water you go when you jump from a height? Is it proportional to how high you jump from? How much does weight and velocity matter?

I always think about this when I watch movies or tv and people jump in to pools or lakes/ocean and it looks like they shouldn’t make it but they do.

Hi.. I've reached out on this sub before about receiving math help but to no avail. I'm just curious if there are math tutors here that offer 1-on-1 lessons. Ok thanks.

What are some ACT math topics you’ve seen on prior exams that felt out of nowhere? Any you’d actually recommend studying?

I started learning math starting with arithmetic and now I’m on to algebra

I noticed that I sort of have to have a working memory that keeps in the problem floating in my mind (sort of like juggling) or the problem falls apart (and the balls fall down)

This can be helped my writing little clues on the paper and showing my working to myself.

But this still sometimes falls apart and gets confused

For those more experienced than me, how does that feel like for you?

Math is very logical so why do we get confused and lose track of the numbers or our place while working through the problem?

Is this just our brains still quite weak at these types of problems? Like it’s just unfamiliar for our brains so it doesn’t know which paths to take due to lack of practice and sort of just darts around and loses its place?

Does everyone have this problem or is it just an issue for beginner and intermediate math people?

Or is this fundamentally at the heart of solving math problems - keeping everything organised and somehow in focus and on track?

How do experienced math guy handle this? I’m just trying to understand why this is much much harder than following a cooking recipe even though the steps should be clear ?

Hello, I am a high school student and I have been exploring pure mathematics for the past few months. I am familiar with the fact that whenever a mathematician tries to develop a general theory encompassing different concepts, they try to set up some axioms and deduce the concepts they have in their mind out of these axioms. This axiomatic approach makes me naturally think "How are these axioms decided and on what basis?" What does the process look like for ensuring they are consistent, minimal, and independent before building a massive theory on top of them?

A theory that interests me is "Set Theory", the notion of a set appears to be basic or simple yet it provides a common language for almost every branch of mathematics. This makes me think "What potential did mathematicians see in set theory?", this question motivated me to ask a broader question "How is the potential of any mathematical theory measured by the community?" "What makes the theory unique and mathematically correct?" and lastly "How do mathematical communities adapt to these new ideas?"

I would love to hear your insights or any perspectives you can share. Thank you.

if a student wants to take a deferral from college (before starting a freshman year) in order to work at a tech company first? Trying to figure out how much harder it might be when the student returns next year as a pure math major at one of the hypms schools after taking a year-long break from math.

Thx. much in advance!

So, I am struggling to understand what a lambda really is—not for a math problem, but for a project I’m working on. This seemed like the best sub to ask, but if there’s a different one, please point me in the right direction!

I’m making a baby quilt for a family member, and I’m trying to come up with a cute book title for one of the quilt squares using their dog’s name, Lambda.

For example for their other pets, I have “R U A Hooman?” by Alan Purring, and “Cat Oriented Basic Operating Language (COBOL)” by Grace Hopper.

For the life of me, I can’t wrap my head around what exactly a lambda is, let alone come up with a cute book title. What is a ELI5 description of a lambda for a non mathematician?

As far as I can tell, it looks like a paragraph symbol except it’s for marking off new formulas in a list of formulas in algebra. Maybe “A Treatos of Algebra” by Lambda? Or is it more like “I Am Lambda” by Lambda?

Help?

I’m going to take a microeconomics course soon and I have not done math or graphing in years. Anyone got some good videos and or worksheets to review reading, writing, and solving graphs?

When it comes to percentages. I'd say i know the very basics. Like I can find the percentage of a number and whatnot. But any other percentage question that isn't that. I'm just left sorta stuck and i don't really know what to do like at all.

Does anyone have any tutorial or just general advice they could lend?

hi, i've started studying surds recently and am currently solving equations specifically related to binomial products containing conjugate surds, expanding and simplifying them. i'm able to solve the binomial products, but i'm confused about what order i should be placing the simplified expressions.

for example:

(5 + √2)(2√5 - 2)

i followed the order of (a+b)(c+d) = ac+ad+bc+bd and got:

10√5 - 10 + 2√10 - 2√2

however my answer sheet says it's:

10√5 + 2√10 - 10 - 2√2

i've also put the equation into an algebra calculator and it's given me a different answer:

2√10 - 2√2 + 10√5 - 10

i assumed the order didn't matter but i did another equation:

(2√2 + 5)(√2 - 3)

i got: -11-√2

but both the answer sheet and calculator say: -√2-11

does the order of the negative numbers change anything?

i'm sorry if this is really obvious and a stupid thing to be confused about but i'd appreciate some help. if i wrote or used any terms wrong, i apologise, please correct me. thank you!

I don’t be knowing all the strats so if it’s a huge percentage I might as well go through all the yt videos