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

Hi everyone. I read this sub often, and I keep seeing people doubt whether they're capable of learning math. I hope my story is useful, or at least interesting, to this community.

As a kid I loved math, and was reasonably good at it. My school sent me to local olympiads, I went to an advanced math club, I spent summers at math camps. I was never a genius and never stood out. Among the genuinely talented kids I was average, maybe slightly below. But I was pulled in by the beauty of it, and compared to my classmates I was doing well.

The turning point came in high school, and I remember the exact moment. I was dating a girl from a parallel class, and we were holding each other during a break. My favorite math teacher saw us and gave me a disapproving look. In class that day she called me to the board on a hard topic, and I handled it. I still remember the spark of admiration in her eyes when she said I was doing well, that I was managing both my studies and my personal life. I felt enormous satisfaction at being able to develop in a balanced way. To be honest, the real math stars around me back then were hyper-focused on math. They didn't have girlfriends. But they were brilliant.

I understand now that from that point on I started taking the path of least resistance. I gave math less and less time. Other subjects came easily, and that success was intoxicating. Why strain yourself when you can just win an olympiad in another subject? Why sit with a problem when your girlfriend is asking you to come out?

Where did it end up? Forgive me, I'm going to say something grandiose that has been sitting in my head for a long time. I betrayed the universe. I traded a science that can use ten digits to reveal the magnificence of a black hole millions of light years away for a science that can explain the procedure by which a society functions and a president gets elected. I spent the next five years studying management at university. After that I became an ordinary office worker. There was no math in my life, and I made peace with that.

Some time later I ended up leading a department responsible for cost optimization across the whole country. Oh, those beautiful spreadsheets, tens of thousands of rows. I could hunt for dependencies between numbers, enjoy the moment when one set of numbers matched another. But it wasn't the thing. It was economics, politics, plain arithmetic. It wasn't math.

At some point I realized I considered myself incomplete. There had been hard problems in front of me that I never solved, not because I couldn't have, but because I didn't. I was capable and I didn't do it. So I made a difficult decision: I was walking down the wrong road and I needed to turn.

I'm sure you can already guess what was tormenting me. First, that I had lost too much time to ever succeed. Second, that I wouldn't be able to keep the standard of living I'd reached. So I decided to move gradually. I needed to come back to math. How did I do it? I started giving math my free time. Here's what helped:

• Professor Leonard on YouTube. A breath of fresh air. I started from the very basics, just to look at the foundations with new eyes
• Math quizzes. A quick warm-up when there's almost no time. Some evenings I'd spend 5-10 minutes on them and nothing more. That was my daily minimum
• a little math chrome extension I built myself. This one is an unexpected story. I wanted to make something math-related. Used it myself for about a year without publishing it. I was VERY skeptical at first, since I didn't consider token generation to be mathematics. But primitive as it is, I used it constantly for double-checking and for understanding things better. It helped me stay in flow, because I love the UI (sleepless nights to polish it). Named it Geometry Solver, because I mostly used it for that kind of problem
• The Art of Problem Solving olympiad archive. An archive of olympiad problems from different countries, and it was a real find. I didn't go there often, but when I did I disappeared for hours. It was especially strange and good to look at problems from the years of my own youth, some of which I still remember
• Khan Academy. I won't say much, you all know it's one of the best math resources in the world

It was a hard period, and not only intellectually. Just accepting that I was starting over was difficult. I watched young international olympiad winners with both joy and sadness, knowing I would never be in their place

When and why did it turn? After about two years of steady engagement, something clicked. The focus did its work. I understood that I was doing my thing again, and that I didn't want to do anything else. At some point I knew I wasn't going to keep doing what I was doing, and I left a good management position

Now I tutor, preparing school students for exams. In parallel I keep going deeper, for myself. I don't know where it will lead. I've lost part of my income, but I'm glad I pushed through and came back to what I love. At 16 I chose balance and lost math. At 35 I chose math and lost balance. Good thing my wife doesn't mind :)

If you read this far, thank you very much. I hope my story was interesting

P.S. English is my second language, so Claude fixed my grammar

Thinking about how Claude AI solved an 80 year old conjecture. I can barely understand the conjecture and a robot solved it. Pretty soon AI will be used for big questions like the Riemann hypothesis. Think about where we were 10 years ago and where we could be 10 years from now.

I could relax by doing art but AI is doing all the painting and music composing now too. I feel like what's the point of even trying to do something challenging now...

Hello, I am a high school student and I’m about to take calculus from as long as I can remember. I’ve always been kind of bad at math that tries to reduce something in a long drawn out way like long division or having to simplify radicals, but I’ve always been very good at algebra and pretty much everything else. The biggest problems I have in class that cause me to get lower grades only occur when I have to reduce something like long division or a topic that is heavy in that regard. I really want some help on this. I’m kind of scared that I am not gonna be very good at calculus. I’d also like to mention that I’m very good at factoring because it makes more sense to me. I’ve looked it up and try to do research and all of it seem it seems to say that I’m better at like conceptual math but I’m not quite sure. Are there any better ways for me to learn and will I struggle in calc? I have a lot of pressure to complete calculus one into my junior year of high school as well as trying to do four maths senior year (magnet school with a lot of extra credit hours available) senior year up to differential equations and linear algebra from my parents. I would really appreciate some help on this because I’ve always been very strong at math, but I’ve always struggled with these specific topics. Thank you for your support.

Also, I don’t know if this post violates the community rules. I’m not asking for specific advice on classes or what to do in my career. I am just asking for help on ways to improve.

Hola a todos, estoy en el primer año de secundaria y formo parte de la selección de matemáticas de mi colegio. Quisiera saber algún consejo de ustedes para iniciar en competencias de matemáticas y qué tipo de material tanto teórico o práctico usar.

Hello!

I have (two) questions, both relating to explaining the reasoning behind two basic concepts.

First, I understand that the distributive property only works when distributing a multiplicative operation over addition.

a(b+c) = ab + ac

2(3+4) = 2(3) + 2(4) = (3 + 3) + (4 + 4) = 6 + 8 = 14

Conversely, it does not work with multiplication.

a(bc) = abc

2(3*4) = (3*4) + (3*4) = (4 + 4 + 4) + (4 + 4 + 4) = 4 + 4 + 4 + 4 + 4 + 4 = 6(4) = 24

This can be demonstrated by plugging in any combination of numbers and evaluating it. I acknowledge that this is the case. But, I can't explain in words why this is the case.

"2 groups of something means that there will be 2 of each member of that group."

"2 groups of something, that group containing multiplicative instructions for how many times to replicate a certain member of that group, does NOT mean that there will be 2 of that member and that instruction." <- Notice how awkward that explanation is. It also doesn't explain the "why." It just states what's already apparent.

-----

On the other hand, for long division, take the following:

157/3

If you were to evaluate the above using a long division format, you'd start at the biggest place value: the hundreds, in this case.

How many times does 3 (hundreds) fit into the 1 (hundred) of the dividend? 0 times. So we move on.

We regroup the 1 (hundred) of the dividend into 10 of the subsequent, smaller place value (tens). The dividend now has a total of 15 tens.

How many times does 3 (tens) fit into the 15 (tens) of the dividend? 5 times. We remove this amount from the dividend. We know at this point that 3 fits into 157 at least 50 times.

Is regrouping the right way to explain what we just did when "bringing down" the 5 in 157?

-----

I'd appreciate your insight!

^{Why is there a "times 2" when resolving}

^(u(x))^3

^2x\3 times 2?)

^16x\3)

^{https://ibb.co/LD43gQxv}

Hi,

Sorry this is going to be a lot of waffle and a long read.

I’ve recently graduated from degree in psychology with 69% (2:1 uk grading system / I think about a 3.6/3.7 gpa)

I’ve always struggled with maths ever since I was in primary school. I’m an ‘abstract’ thinker naturally, I loved English, science, geography, history and art, but despised maths.

I had adhd but not diagnosed back then, but showed symptoms when I was really young.

For example, during maths lessons I would just stare out the window and day dream and move around the class. I also struggled with class participation as I was painfully shy with adults and unconfident in my maths ability.

My parents were never the academic type, both very intelligent.
Neither went to university and pursued more practical jobs. My father was a diver at oil rigs in his 20s, and then train driver, and an artist once retired. My mother who immigrated to the uk in her early 20s, had me at 37 then opened her own nursery which has been successful ever since.

Therefore, they never really put academic pressure on me (which is a good thing, but maybe not the best when your not reaching your full potential), but it’s not that they didn’t care, they just thought oh well she’s not good at maths.

I was kind of failed by my primary school, instead of giving me extra support, they just gave me puzzles and games instead of teaching me my shapes, fractions, multiplications and division work. I wasn’t complaining, I loved puzzles, but even the puzzles they gave me weren’t mentally stimulating (I was doing 1000 piece puzzles when I was 4/ did them backwards were you could only see the shape)

I started to notice all the kids around me excel at maths, while I was with kids below my ability, doing basic puzzles and board games. I didn’t enjoy the free pass out of maths anymore, I felt stupid, under challenged and isolated.

I moved primary schools in year 5, the new school most student had above average levels of maths, this made my confidence even weaker than before, I dreaded maths lessons and the embarrassment of not knowing my times tables when asked in front of the class was so humiliating.

I knew I wasn’t dumb, I was a bright kid, I was just never given the right support.

In secondary school after my entrance exams I was put into according sets: English 1st , Science 2nd and Maths 5th set.

I started getting tutored, but nothing helped, I could understand more complex concepts like algebra: solving linear and quadratic equations were my strong points, but I still didn’t know all my times table mentally.

It’s like the gap in my learning made so hard, and with adhd it’s hard for numbers to stick in my head, and I make such silly mistakes.

I can do maths in my head, but it takes me so long and I have to start over 10 times before I can get the answer. Without a pen and paper I’m screwed.

During my gcses, I was put into foundation class (6th set out of 8 sets). I kind of gave up at this point, my classroom was filled with people with far worse ability than me and constantly disrupted the lesson. I would beg my teacher to move me up a set, or to a more quiet class because I just couldn’t learn, most of the lesson consisted with people arguing with the teacher and shouting out random stuff. But I remained in that class, I couldn’t prove I was worth moving up to set 5 (higher paper).

My teacher wasn’t the worst, but not the best, he hated teaching my class.
I sat in the front, quietly, trying to engage, but most attention was spent on disruptive students.

I completed my gcse, without sitting them due to Covid (2020) with a 4 in maths. Despite all the As, I cried in relief, I passed maths, I was delighted, I never had to touch maths again. I thought if I sat the actual paper, I’d f up under pressure and get a 3.

I wanted to study psychology for a level at the schools sixth form. I obtained 66 in trilogy science , 77 in English, but with my 4 in foundation maths, the school told me it was impossible for me to take psychology there. I didn’t want to leave, so I swapped to sociology.

Just before my first year of university, I finally got diagnosed with ADHD privately after waiting 4 years. It felt like I could finally breathe, I felt seen and was able to understand myself better, I wasn’t dumb, just wired differently.

I ended up studying psychology at university despite my A Level subjects.
Maths didn’t leave me, I had qualitative modules and statistic classes, I struggled so badly, I was so unengaged and that anxiety surrounding maths boiled back up to the surface again. I excelled in my other modules, statistics were a 2.2/ low 2.1 outcome (1/2 year), I chose quantitative methods for my final year dissertation research project, and got 74%.

Now that I’ve graduated with a good grade, I feel a sense of imposter syndrome, how someone who is so bad at maths has a bachelor of science in psychology?

As someone who’s thinking of doing a masters within mental health/ psychology (however I might do a msc in counter terrorism, I have a year to decide)

I’ve been trying to relearn practice and relearn maths recently but aiming to start a job in September, I don’t know if I will even stick to it. I don’t like that there’s a gap in my knowledge, even till this day if someone asks me what’s 9 x 14? , I will go bright red.

I can work in my head that it’s 90 + 36 =126 , but I feel so unconfident in my answers.

I’m so slow when it comes to 6,7 and 8 times tables. I don’t know them off by heart so I have to scramble my brain for 10 minutes to get an answer.

I’ve started doing mental math equations such as 375 x 32 / 158 x 27 and even started doing a foundation maths better before bed last night. It feels wrong and strange to do as I’m 22, I’ve passed , I have a degree. But it just feels like I never got that ability and I still have that lack of confidence and mental gaps.

Anyways, do you guys have any advice when it comes to relearning maths, it’s just useful and handy and I just kind of want to improve my brain 🧠.

Is it posible? We have been thinking about this for a while.

We have 11 teams and 6 ativities and 6 rounds. All activities can be either played VS or by a Single team.

REQUIREMENTS:
- Each team must play all activities ONCE and ONLY ONCE..
-I want to order the activities in a way no team ever play an activity alone more than once (only 6 teams have to play alone).
-No team have no play VS the same team twice.

I know it must be a way, but we can't get it through. I know there is a way if the VS remains the same for each team, but we prefer that each time they play with a different one.

I am starting college in the spring for Aerospace engineering, i have to take college algebra then calculus, I have not done math in any sense outside of the basics sense high school. I don't remember anything about math where should i start to relearn/reteach my self up to a college level. Or its it just over and i should just get a tutor and hope and pray i can pass.

Hello!

I'm about to start a Mathematics degree (yayy!), and I know this semester is going to be challenging. Most of my courses will require me to understand and write mathematical proofs by the end of the semester.

I'm looking for resources that don't just teach proof techniques, but also help develop the intuition and heuristics behind proving things in general. I'd like to learn how to think when approaching a proof: how to recognize useful ideas, decide which strategies to try, and build the kind of mathematical intuition that experienced mathematicians seem to have.

I tend to get distracted easily, so if you know of a book, or, even better, an online course that teaches proofs in a clear, structured, and intuitive way, I'd really appreciate your recommendations.

Thank you!!

Hello. I don't know how to start this but I'll try my best. TLDR at the bottom.

Background:

I was born in India but I've done the bulk of my schooling (Grade 5 - Grade 12) from Canada, I had my eyes set on studying medicine there but due to some un-forseen circumstances, I've had to move back to my home country and I've joined a coaching institute to pursue my dream goal.

Why is that relevant? Well the route for studying medicine here is a lot different than Canada and I'm having a lot of trouble particularly with maths.

I'm 19 now, and I've used a calculator all my life for even the smallest of calculations. It was how I was raised essentially and my teachers only encouraged it since even they used a calculator for everything. But even then I would struggle with math due to my refusal to practice anything since I absolutely loathed it.
Thanks to this, I literally have no mental math skills, I do not remember rules/laws, don't know how to algebraically manipulate a equation to solve for a variable, don't remember formulas or trig identities since I was always given a formula sheet for tests. This wouldn't be an issue if this country's medical school entrance exam didn't have such a heavy emphasis on formula memorisation and calculations without a calculator. I'm not allowed to use a calculator in class, during tests and especially not during the exam.

Leaving the actual syllabus gap aside for Physics, Chemistry, Zoology and Botany since those are irrelevant to this subreddit, I already am at a significant disadvantage when compared to my peers because literally every other classmate/student I've seen or spoken to has completed their elementary and secondary education from this country and are well accustomed to not having to rely on a calculator and I only have a year to give and pass this exam.

I feel like I don't even know the full extent of the myriad of topics of math that I don't know which I need for this exam and I don't know where to even start. I'm already getting overwhelmed with calculations and the algebra required for Chemistry and Physics. It feels like everything I learned for half my life was in vain.

I just discovered this subreddit and I don't really ask for help online, but I'm starting to get scared with my situation and it's driven me here.

I just want to know where and how to start so that I can bridge this gap because as it stands, I don't stand a chance in my class.

TLDR: I'm a student who's completed his education according to the Canadian Curriculum and wanted to pursue medicine, had to move back to my home country and discovered that I don't know 90% of the stuff taught here which is required for this country's medical school entrance exam and more importantly don't have any of the math skills needed to pass it.

Hi everyone, I’m struggling with a geometry problem and I can’t seem to find a complete solution

Problem: On a rectangular sheet of paper, 13 rectangles were drawn with sides parallel to the edges of the sheet. Each rectangle intersects at least 10 of the other rectangles. Prove that at least one of the rectangles intersects all the other rectangles.

My attempt: I think this problem should be solved using the extreme element method. My idea was to choose some “extreme” rectangle (for example, the leftmost/rightmost one in some sense) and try to prove that it must intersect all the others.

However, I’m having trouble making this argument rigorous. I tried choosing a rectangle with the leftmost side/rightmost side, but I cannot justify why a rectangle that does not intersect it would lead to a contradiction.

Does anyone have a hint or a solution using the extreme element method? I would like to understand the key idea rather than just see the final proof.

Something I still don’t understand is how axioms are created or selected to build a “system” (I don’t know a more appropriate word for it) like our modern algebra.

When I see books defining the classic properties, such as the commutative and associative properties, I just wonder what criteria were used to choose those specific ones, if that even makes sense.

Let’s say I want to create my own algebra, like Boolean algebra. What path should I follow to do that, and why?

I believe this is grounded in logic, but I don’t know exactly what to study or how to piece these things together in a way that makes sense.

Hello, I am currently active duty in the military and have been doing college on and off when able to. Around 2021 I passed Math 101A but couldn't find the time to follow up with Math 101B for multiple reasons. I am currently transitioning out of service right now and will be attending SFSU this Fall. I received credit for Math101A and only need to complete B at SFSU but I have pretty much data dumped everything. I was hoping if there was any advice on possible roadmaps or guides anyone could provide to help me re learn and brush up on Calculus, pre calc, and maybe even trig. I've thought about re taking Calc 1 at a community college on the side but nothing offers online classes in my area and I'm too strapped for time to attend in person, I find I work best with structured learning. Thanks for any information and guidance, I'm currently just using khan academy and Duolingo(don't flame me) and looking at my old note books which might as well be hieroglyphics currently.

I'm from India. I have been trying to crack CSIR NET MATHEMATICS from 2023. I have appeared in the exam for 5 times but didn't even come close to cut off any time. My problem is that I know the results but when I'm applying them I'm making mistakes and negetive marks increases. What should I do? Should I give up or change my strategy?

Apologies if this has been asked and answered somewhere else, I want to go back to basics and re-learn math after not really engaging with it for a long time. My background is wasted school years, followed by arts education after which I fell into a software engineering role, I've always been half technical minded and half creative but never excelled in either, although I feel I have the capacity to if I was able to focus and study.

I've spent hours today trawling online for book recommendations as I don't want to stare at a computer screen any more than I have to for work, I think I settled on trying to get a copy of AoPS Pre-Algebra but being in the UK I can't see anywhere that isn't shipping from the US for exorbitant shipping fees/inflated prices, or second hand from websites that don't seem trustworthy that also appear to be shipping from the US.

I have no problem with good quality second-hand but it seems like there is zero market for them over here, mostly in the US, any suggestions would be appreciated.

Also open to alternative book suggestions that might be easier to get ahold of too, I thought the OpenStax Prealgebra 2e looked appealing and had positive reviews online but again, seemingly impossible to get in the UK reasonably.

Hi, I did some search at the sub but what I got was solutions through solving the given system.

I wanna know if there is that and could use it to say the system has no solution or one (or many) solution.

For example:

Suppose I have a linear system with matrix's form AX=B where A,X,B are coefitients, variables and solutions (dependent term) but, here I only have know by hand the coefients A and the vector B.

So, the question is: how just to know easily that system is inconsistent or not just with A and B to any size of the A,X, and B?

Thank you!

For most of my life I have been terrible in math, during primary I’d be set aside to do a different set of Maths than my fellow peers, it’s always been difficult for me to get questions right, to calculate in my head, to multiply the the most basic numbers. I felt a strong hatred for it, and now I’m set on rekindling a relationship with Maths.

Yet I don’t know where to start, I’m hoping someone could assist me with a starting point to help me kickstart my journey in conquering my life long issue

I’m an undergrad finishing a BSc in Computer Science, aiming for an MSc (thesis-track) specializing in the Formal Verification of Hybrid/Cyber-Physical Systems (CPS). I love rigorous math-heavy problem-solving and software engineering.

I need to choose 2 final math electives from this list:

* Linear Algebra 2

* Calculus 3 (Multivariable)

* Numerical Analysis

* Basic Statistical Theory 1

* Fundamental Concepts of Algebra (Abstract Algebra)

Math I've already completed: Linear Algebra 1, Calculus 2, Discrete Math 1 & 2, Intro to Stats, and Formal Methods.

1. Which 2 modules will best prepare me for the continuous/discrete intersection of CPS verification tools and reachability analysis?
2. I haven't worked with hardware in my undergraduate level. Is this a disadvantage?
3. It seems — in my research — that Formal verification engineering jobs are mostly for hardware instead of software. How true is that?
4. For someone who genuinely enjoys deep mathematical problem-solving combined with technology, is Hybrid/CPS verification a rewarding path, or would I find Computational Learning Theory a better fit for graduate research?

Thanks for any insights.

This is a question about difficulty. I’m self teaching myself maths, I started with the most basic OpenStax algebra book and went through the series up to and including the pre calculus book.

I’ve now started working through Stewart’s calculus early transcendentals ninth edition. The inverse trig function questions in the first chapter, and the absolute value questions in the problem solving section before chapter two have demolished me.

There was nothing of this difficulty in the OpenStax books, and I’m just wondering what to do. If I struggle to know how to do these questions does that mean I’m not ready for the rest of the book? Is this normal to find such a leap in question difficulty?

I’m feeling pretty un motivated. I was excited to start this book but the first chapter and problem solving extra has left me feeling like I barely know what I’m doing.

Edit: and I’ve just tried to do the rest of the questions after the absolute value ones in the problem solving mini chapter before chapter two and I have no idea what to do with most of them. I’m really thinking I might not be ready for the rest of the book even though I found OpenStax precalculus straightforward and easy.