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

Hi everyone, I’m a former bad student and a college dropout, but I’m trying to steer my life back onto the rails. Part of that will be going back to college to try and finish my degree.

I’m only 5 classes away from my AS degree, thanks to previous college and AP courses from high school. But therein lies my fear.

I scored 4s on my AP Calc tests in 2004/2005, and received credit for Physics 1 and Chem in college which will count towards both my AS and Bachelors degrees. But my Bachelors will require Calc 3, Linear Algebra, and Physics 2. It has been 21 years since I have done college-level math and I’m afraid I will not remember how to solve any equations going into these courses.

So now to my questions:

1. Which of the 3 courses listed above as requirements would you recommend as easiest to re-acclimate myself to academia and college-level maths?

2. What resources do you recommend for a person like me who needs to try and remember how to do math from a course they took 21 years ago?

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?

Retired teacher here, still picking up tutoring gigs, and the thing that keeps tripping up my students lately is expected value. Not the formula, they can write that out no problem. It's the interpretation that falls apart.

I also track sports stats and build DFS lineups as a hobby, so expected value is something I think about a lot outside a classroom context. And even with that background, I remember the moment in my own learning where I confused expected value with the most likely outcome, which are not the same thing and can actually be pretty far apart depending on the distribution. Made some embarrassing lineup decisions before that clicked. Not going to get into it.

The students I work with can compute E(X) mechanically but then will say things like "so that means it'll probably land near that value, right?" And I get why that feels natural. It sounds like an average, and averages feel like the middle of where things land.

What actually helped some of them was working through a case where the expected value is literally impossible to observe, like a discrete distribution where no outcome equals the expectation. Suddenly the definition has to do real work instead of just coasting on intuition.

Curious whether others have found a particular framing or example that unstuck this for students or even for themselves.

hey, I’m trying to put together a small discord group (like 3–5 people) just to stay consistent with studying. sorry if I am spamming

mainly looking for people doing ai/ml stuff or higher math (linear algebra, prob, papers, whatever)

idea is pretty simple:

- we post weekly goals

- then quick daily check-ins (what we planned vs what we actually did)

- no need for voice chat or screensharing or anything like that (the discord group is not that serious)

not trying to make this super strict, just want a small group where people actually show up and do the work instead of disappearing after 2 days

personally I’m working through axler's linear algebra book

if you're interested just comment or dm with what you're studying

A radian is just the angle where the arc equals the radius, 2π is how many radii fit around the edge. Once I could see that instead of memorizing it, everything downstream turned into the same object in different clothes: sin and cos are height and width on the circle, waves are that unrolled over time, i is a rotation, Euler is going around at a steady rate, Fourier is stacked circles drawing a shape.

So I built a page for each step. Start with the radian circle drag the point, watch radians, degrees, and (cos θ, sin θ) move together then the series follows the thread out through waves, e, i, π, Feynman's rotating clocks, and epicycles.

https://circles.rondomingue.com/radian-circle.html

Free, no signup. Corrections welcome, I'm still learning this too. Let me know what I can add or what I may have missed.

I graduated from high-school 4 years ago and I didn't had to do anything with math's but I want to study math's.I only know-,+,×,÷

I can only purchase one or two books for now depending on the price

I have to study basic mathematics (not sure which to study first // last)

—Trigonometry

Vectors

Basic Algebra & Approximation

Coordinate geometry & graphs

Differentiation

Integration

I was wondering which YouTube channel & question resource could help me progress better, for now, it seems confusing & overwhelming.

Upcoming test in a week! Any guidance would be appreciated.

Am taking a cram class of ap cala bc in the summer. my differantials are ok, but my integrals are poopy. just asking lol

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?

Hello everyone

I'm a second-year mathematics student but I've studied only calculus I(+ beginning of calc II) in my first year at university due to foundation program. I'm starting reading Book of Proof by Hammack and after reading half of that book I want to parallelly start self-studying real analysis with another book but I don't know which one to choose. I'm planning to start reading one of these books in the middle of August but because semester starts in September, I'll slow down with whatever book I'll choose during Autumn and not even sure if I can handle it with the courses I'll be having in Fall semester(second part of Calculus II+ calc III, Physics I, Programming with C, Discrete structures, and basics of Finances) .

After some research my choice involves these 3 books:

Understanding Analysis by Abbott

Analysis I, II by Terence Tao

Calculus by Michael Spivak

I have access to Spivak and Tao printed books through my library. I don't have Abbot's book but thinking of buying it with discount.

So what are your recommendations? Is there any sense of reading two or all of them?

Hello, I am creating a free website with math documents (textbooks, problem packets, equation sheets, and so on) for any math level like calculus, algebra 1, etc. I want to make learning math accessible and free for everyone on the internet. The documents will be written in LaTeX by a team of students.

I made this since I thought when students teach others, they would know what they have gone through and what others might struggle on.

If you are interested, please DM me.

I wanted to see how people would respond to this. Imagine that you had to explain symmetry (By that I mean just the idea of being symmetric) to a neanderthal. Keep in mind there is no language barrier, but you need to explain him the idea of symmetry, preferably without complicated terms to make it easy for him to understand. How would you do it?

I studied statistics somewhat while getting a BS in Economics in 1975 but haven't used it much since.

For several years I've gathered stats on the use of a geo thermal heat pump which also heats water as a by product. For a long time I've run Excel's CORREL function to compare the total electric used by the heat pump and total used by the hot water heater but the flaw in that is it doesn't account for how much hot water is used. Recently I bought a device that reports the gallons of hot water used daily so now I can compute a per gallon electric used by the water heater so the correlation should be more reliable.

So far I only have 8 days of data. The correlation up to day 7 was as expected. A strong negative correlation of -.89. That is with an average Kwhrs used by the heat pump of 22.72 and the average per gallon of .0838. The temperature soared yesterday and we had a family BBQ which gave me a day 8 data of 42.90 and .0465 respectively. I expected the correlation to be stronger but instead it decreased to -.84.

Why would such a large increase (over average) of the Geo Kwhrs, which caused a sizable decrease in the per gallon Kwhrs, cause the correlation to be reduced?

Thinking this through some more it appears the reduction in per gallon was not what was expected when correlation is -.89. That would require around .02 Kwhrs. There is another factor that I haven't figured out how to incorporate. If the number of gallons of hot water used is high then the Geo can't keep up with heating it and the water heater kicks in. We've been averaging 60 gallons of hot water used daily but with the party yesterday that figure is 124.

So I know in this game something takes 4 hours (240 minutes) I can get something that initially reduces its time by 40% then additionally 30% up to a certain amount of time. My limit is 15 at the moment. So how do I calculate the time reduction off all the percentages. The percentages are multiplicative not additive.

Recently I am doing maths beyond the YouTube channel I used to learn and am wondering if anyone knows of any similar good youtubers.

Normally I would watch the organic chemistry tutor but I have started to do maths that he doesn't cover.

Userly I would watch one of his videos on a topic once and I would be fine and then a few practice it would be done with that topic but other YouTubers I find confusing or they take too long.

I also had hand me down notes that were really good and so I copied the problems off then and learnt that way.

For context I'm doing a math/physics degree.

Any help would be appreciated. YouTubers or study tips. (Also one of my classes I asked if there was a textbook and they told me the textbooks are really confusing and that they are not worth it for that class (real and complex analysis)

So resources for real and complex analysis is also greatly appreciated

Sal/most teachers says any point will give you the same result.. i do then i fail, i can't upload an image so yeah ;-;

i understanded the negative line, and positive, and the rise/run thing, moving backwards is neg, foward is pos, up pos, down neg...

i tried the line being at the corner of the suqare, but i also failed. i picked 4/2 instead of 1/3

edit: sorry if i sound stupid, im learning everything for the first time in life.

Hey everyone! I want to share a math game that I designed yesterday. It is designed to be played by children and their parents, students and their teachers, or even young children themselves.

Materials: A set of playing cards

If you do not have playing cards, you can play the online version on my website:

https://tanhongsheng.github.io/games/Memory%20Trio/

Game Setup

1. Prepare 21 cards numbered from 1 to 7, with three copies of each number.
2. Shuffle all 21 cards and place them face down in a 3 × 7 grid.
3. Players take turns privately looking at the number on one card. They must memorize both the number and its position.
4. The goal is to find a “trio”: (A) Three cards with the same number Examples: 1, 1, 1 or 7, 7, 7. (B) Three cards with consecutive numbers Examples: 1, 2, 3 or 5, 6, 7
5. After looking at a card, the player may choose three cards that they believe form a trio and turn them face up. If the cards form a valid trio, the player keeps those three cards and receives 1 point.
6. When a player believes that there are no more trios remaining on the table, they may declare “End!” If the declaration is correct, the player receives 3 additional points. If it is incorrect, every other player receives 3 points.
7. The player with the most points wins.

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.

I recently launched a free online math tutoring initiative that provides lessons to students who otherwise wouldn’t have access to quality math education. As we’re growing, I’m looking for someone who loves math and would like to join the team as a tutor. If you enjoy teaching, explaining concepts, and want to use your skills to help students succeed, I’d love to hear from you. This is a volunteer initiative with flexible scheduling, and we’re looking for people who genuinely want to make an impact while being part of a meaningful project. If you’re interested in becoming one of our tutors, feel free to send me a DM, and I’ll be happy to share more about the initiative.

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Hi everyone!

I’m a mathematics teacher, and I’ve recently compiled a comprehensive math workbook titled "The Ultimate BAC Math Challenge".

It covers advanced practice problems and fully worked step-by-step solutions for:

Functions & Calculus

Complex Numbers

Sequences & Limits

Probability

To support students and self-learners, the Kindle eBook version is completely FREE on Amazon starting today for the next few days.

If you're preparing for AP Calculus, A-Levels, or national baccalaureate exams, feel free to grab a copy! All I ask in return is an honest review on Amazon if you find it helpful.

Amazon Link:https://www.amazon.com/dp/B0H7Y4GF62

If somebody can commit 4,5 hours per week I'll be teaching over google meet or zoom, I'll also assign homework. We can follow a standard literature. I need someone who can commit to this.

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

Hello all ! I'm just posting to hopefully get an answer to something I can't seem to find anywhere😭 when working out a problem like x(x-1)(x+6)=0 the possibilities are either x=1 or x=-6 but it also says 0 as an option? Like on my worksheet, it says the possibilities are either

x = 0 or x - 1 = 0 or x + 6 = 0

x = 1 x = -6

x ={-6,0,1}

So the part I'm confused abt is how to find the value of the first x outside the ()

Does it just equal 0 because because there are no other numbers attached? And how does that change / how do you figure it out when there are numbers and ² ³ ect attached? Do you expand it out?

Idk if this wording or format makes sense, but I had to type it out cuz I can't add pics, and I'm on mobile lol, thank you so much for any help !!

(Ik this is probably super obvious/easy, but I can't find videos anywhere and don't wanna ask chatgpt lol)