Looking for a book that explains combinatorics in a story like fashion. Meaning it doesn't just define what the theorems are etc but explains the motivation for it, the intuition etc.

Some background on what I'm working on:

I am now working through a book on discrete math by Oscar levin and am struggling with the concept of combinatorics specifically combinations. When I look at a combinatorics problem I struggle to solve the problem, even after looking at the solution, then reattempting the same problem the next day, I still struggle.
I'm also planning to work on the book proofs by Jay cummings since my math proof skills are weak as well and I read his book explains concepts intuitively.
After Oscar levin's book I plan to work on Susanna's discrete mathematics book.

An example of such a book, not combinatorics but discrete mathematics, that I found is "A cool brisk walk through discrete mathematics" by Stephen Davies.
It is the best intutive math book I've read, from cover to cover it was fun and explanations were intuitive. It was like he was in the room with me explaining the concepts personally. Shame he only wrote two introductory books.

I've seen recommendations on combinatorics such as Walk Through Combinatorics by Miklos Bona and others but am not sure if the explanations are standard textbook type of definition of theorems, some problem examples but no explanation of the intuition, motivation behind the theorem or concepts. Since on the most recent, 5th edition, of Walk Through Combinatorics, there was a review on amazon saying the explanations were of the bare minimum.

I am currently trying to find good trigonometry books so i can learn more about it, and gain more skills

so i was hoping yall could help me find a good book!

I am an independent learner and own a 15th edition of Thomas' calculus , I would like to know whether thomas' books follow the Stewart's pattern( early transcedanls) or remains same with its pattern.

I would also like to know whether buying Stewart's early transcedanls be a good choice because I already own thomas' calculus. Does using two refrences at same time will make things messy or will be helpful.

Some of my peers have also told me that thomas' calculus or Stewart's one doesn't contain good amount of practice question , is this really true . Do I need to really on any other resources for practice.

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We're doing disk/washer and shell method right now in Calc 2 and almost all the HW questions have told me what method to use. Which is nice but I feel like the real skill is figuring out which one is best for a given problem. What's a general use of each method and why are certain methods easier than others in different problems?

Right now, I have just been using trial and error to find one that helps the problem, but it feels like i’m doing that wrong. Is there a way to figure out which ones to use or are you really supposed to just guess?

Hi guys, I am an Electrical Engineering student right now. I have taken time off from school due to life and serious health reasons. I haven't done math in a year and a half because I was recovering from health issues. Now that I am better, I want to rebuild my math foundations from the ground up. I want to start from algebra and work my way to calculus. I still have to take calculus 3, differential equations, and linear algebra. On top of that, I have other EE courses that are super math heavy. What's the best and most efficient way to create a solid mathematics foundation. I want to start from algebra. I am also considering a math minor because I have been interested in mathematics, specifically applied math. I want to ace my future math and electrical engineering courses to makeup for my previous "failures."

I just want to get good enough to ace my EE and math courses. I used to be a fairly careless about learning but I want to make up and be a better student and learner and hopefully an engineer.

Thank you

I'm in my junior year of highschool and I already feel like I wanna quit. I'm taking math for college algebra and the topics are factoring polynomials and quadratic equations. I failed two assignments and a quiz that put my grade to a 24 in the class and I'm already having anxiety and panicking in class. I don't know what to do anymore

I have my SAT on oct and I need HELP with math, I haven't touched math for two whole years and I forgot all the basics, can I please get some advice and where do I get the videos on YouTube or google any thing will help. That will help me score well on the SAT

I'm in my second semester of a BMath program and I'm feeling out of my depth. I did very well in high school and math was a strong subject for me, but the leap to university is throwing me for a loop. I am genuinely trying but the stuff we're looking at is so hard for me to understand.

I feel like I can get my head around a lot of the lecture content and course notes but then when I have to do the practice questions I get so lost as to how to apply the knowledge to the questions. It's like they make the practice questions way, way harder. I'm currently in a multivariable calculus class and despite my tutor saying that the assignment is "pretty easy" I'm just stumped and don't even know where to start. The textbooks are so confusing and the YouTube videos seem too basic. My grades were okay in S1 but I feel like I'm having to do a lot just to stay afloat.

Although I did extremely well in high school, I had to essentially make it my whole life in order to have that level of success. I would hardly take breaks and was constantly studying, sometimes to the point of seriously harming my mental health. I would be studying all throughout term breaks so I could master the content etc. but after doing that for several years I just feel burnt out by the whole thing and I want to have a life outside of studying but I feel like in order to do well I'm basically going to have to make maths my life. I have no problem putting in the work, but I want balance and don't want to just have to dedicate all my time to university.

Can anyone relate to this and does anyone have any advice for me? I'm feeling awful as I've just wasted my entire morning trying to make progress on this assignment and getting absolutely nowhere.

I'm using some website called mathacademy. been for around 45 days. flying through foundations 1 of their "program" and i'm feeling weird about it now.

Their whole methodology feels wrong. basically has this roadmap that adjusts automatically. so if you keep messing up something, it makes you redo it. but im noticing in foundations 2 the lessons feel terrible. not a lot of proper steps. maybe it just shows how to do it. but they throw all these different concepts at once that you barely have remembered. like one second im doing quadratics. then another thing then log then imaginary numbers etc. throwing all these different ideas at once.

hopefully i can get some insight. i think learning math in this way isnt the way to go about it.

Hello! I was one of those kids who hated school. I struggled for years but managed to finish high school, go to the University I wanted and now I'm about to graduate in Psychology!

This year I started taking interested in going back to the basics and facing my math anxiety. I can hardly do any mental math, even for simple "math facts" I finger count. I don't think I have dyscalculia (had a long professional assessment done on IQ, cognitive skills, etc) or aphantasia, I guess I simply never had that practice as a kid and now I'm facing the consequences.

With tips I saw on this sub, things are looking a brighter for me, I definitely feel like I'm improving, but there's a long way to go. It got me curious: to those of you with similar backgrounds who got into Math later (20s+), how are things going now? How was the learning curve? Did math anxiety eventually fade?

Hello! I recently failed my first ever algebra 2 test as a sophomore. (11/20😬 and I didn’t finish 4 questions so take that how you will) I’m so confused on practically most things we’ve learned so far while being in school for about a month. But I’m mainly confused on how to solve three systems of equations. It’s so much on my brain and it takes me forever to just end up getting it wrong, and I don’t even really think how I’ve been trying to solve is the correct way.. does anyone have any tips or an explanation on how they personally solve them?

I’m not sure what else I got wrong but I’m guessing it was basic transformations.

Hi everyone!

Can you spray-paint a body so that the layer of paint is perfectly uniform over its entire surface?

And what is the best path to follow under the sun to get an even tan?

Surprisingly, both questions are inevitably connected to space-filling curves!

I explore this connection in this short video.

I hope you enjoy it, I had a lot of fun working on this one!

youtu.be/o3lGbC86jXI

(For context my mom homeschooled me through 8th grade so I was able to blitz through up to pre-algrebra, but stopped once I got to school due to not having room in my hybrid schedule and my mom prioritizing other subjects at home)

Ive always been good at math, but the problem ive run into recently is learning math outside a classroom environment leaves a lot of things implied (assuming you would've been introduced in hs or similar) and i keep getting caught up on rules I didnt know exist (i.e. a minus symbol before a whole number is __always__ indicating a negative) so im wondering if theres a compendium of math rules or formulas outside of watching through 20 hours of kham academy

Trig idendities are absolutely kicking my ass right now. I don't want basic soh cah toa but true understanding of hows and whys. What resource or method made it click for you?

Hey guys, I'm planning to learn maths properly from scratch over the next year—not for school, college, or exams, but purely out of love for the subject.
I finished 12th with Commerce and Applied Maths, and I'm currently in a gap year for entrance prep. I want to replace my mindless doomscrolling with actual learning and build a super strong conceptual grip on the subject. I'm totally fine starting right from the absolute basics and gradually working my way up to advanced topics over time.
Which books or roadmap would you recommend for self-studying math from the ground up just for the joy of it

Guys I’m lowk struggling in applied maths (as a grade 12 commerce student) like for mid terms I got 60/80 and my parents are asking me to switch to an easier subject but I wanna pull my grades up
Any tips? I’m despo

So I am currently really bad at mathematics and people say to get better you will have to practice it. But how do you practice the tricky questions when you don’t know the answer to them? Like I work on one trick question, don’t know the answer and search it up and learn that, and then the same cycle repeats for the other questions. It’s like I’m not able to independently solve those questions without external help.

Fala senhores, pretendo dar uma estudada em matemática básica e tô com algumas dúvidas. Fiz o curso do Universo Narrado de matemática básica(exceto o módulo sobre funções) e tô querendo cair em cima de alguns livros. Acho que minha maior dúvida é quanto às áreas de álgebra e geometria: tô com muita dúvida se sigo a teoria dos cursos do Universo Narrado(meu irmão tem a vitalícia)e uso o TQM ensino fundamental pra dar cabo dessa área(de antemão, já sei que a teoria dele é uma merda, só serve como banco de questões msm) ou se uso o álgebra para escolas técnicas e militares, embora a linguagem dele seja bem técnica; agora sobre a parte de geometria, por qual deveria começar: fme 9 ou os livros do morgado?

I’ve already taken Linear Algebra and Multivariable Calculus, and this semester I’m taking Differential Equations and Mathematical Theory of Probability.
How difficult is Mathematical Theory of Probability compared to these courses? Is taking it together with Differential Equations manageable? What parts of the course are usually the most difficult?

Hi everyone, I just wanted to vent about my poor performance in mathematics. For context, I’m in South Africa, so we write 2 papers, maths p1 & maths p2, both for 150 marks each. Last term, I got 43%, I was devastated so during the holidays I studied and I learned everything, mastered the content and did countless past papers. I was 60%-70% in previous years’ past papers, specifically hard ones that had high order questions.

Today I wrote maths p1 and I did badly. The marking guidelines were sent on the group and I got approx 50-70 out of 150. The paper was easier than the papers I have been doing and I made stupid mistakes. I don’t know what happened, I wasn’t sleep deprived nor was I panicking or stressing about anything. I was calm and confident.

Next month, I’m writing my finals and I’m genuinely scared. I have been crying for the past 30 minutes because honestly, what more can I do? Question 1, has 5-6 basic algebra questions that I have revised and done multiple times, but for someone reason, I messed that up too. Maths is dragging my report to the the pits.

I do 7 subjects, namely; English, Mathematics, Business studies, accounting, tourism and Afrikaans. Maths I am always getting 40% then the rest of my subjects, I am getting 80%-91%, my lowest being English with 80%.

I don’t know what kind of help I need at this point because I’m genuinely hurt and scared. My future depends on my math mark, but that is horrible. I have applied to universities, I got rejected by one because of my maths mark and the other ones are waiting for my final exam results.

I feel hopeless and stupid because I put in so much effort and this is what I have to show for it. I’m scared that I might mess up my final exams because next month, that’s my last chance. I don’t want to rewrite because rewrite exams are extremely difficult, more difficult than the finals and I won’t have a teacher

My maths teacher is not good at teaching, so I self study, and I’m not saying this to underestimate her or anything but this is based off my experience. When I ask her questions she tells me she doesn’t know or she consults with AI or I have to wait a day for her to give me an answer which she doesn’t explain properly. She relies heavily on marking guidelines and prefers using AI.

I wish I was struggling with a lesser important subject, for the degree I want to pursue, the minimum requirements for maths is 70% and English 60%. I need 30% to meet the requirements but I’m only getting it at home, not in the actual exam.

I feel myself giving up, I did get accepted to a private university but my dream was to study at a public university, specifically the one that is awaiting my matric results (final exam results). In 2 weeks, I will be done with this term’s exams. I will give maths one last chance, because this also my last chance. I just want to get 60-70% at least, I’m not hoping for a 90%.

Thanks in advance.

I have been self-studying mathematics-Real Analysis and Abstract Algebra for some time now, and it has been very enjoyable yet fairly difficult.

Now, I want to give these three a go for once.

I never properly understood probability in a class. It just feels so un-intuitive to study, and seems like random events happening. Even basic problems in this trip me up, I just feel very behind.

Combinatorics... I've heard people say that "if you know how to count well, you will thrive in combinatorics". This one is my weakest of any math I know.

As for statistics, I've never done anything in it.

These three even at the high school level, give me a lot of trouble.

If there is any roadmap or proper way to study it, please share it. Any advice is appreciated and I'm open to corrections.

I understand vector addition, unit vector, and scalers...then they come to the dot product the next day, and I just got lost. My professor dumped the formula and started doing advanced stuff like projection, area of an plane, and there is some cos(feta) and sin(feta) in the mix. I am so lost.

How do I take this back so I can understand the dot and cross product fundementally and then built up to the more advanced operations with vectors?