/r/learnmath

Post all of your math-learning resources here. Questions, no matter how basic, will be answered (to the best ability of the online subscribers).

We're no longer participating in the protest against excessive API fees, but many other subreddits are; check out the progress among subreddits that pledged to go dark on 12 July 2023 and the top 255 subreddits (even those that never joined the protest).

We're no longer participating in the protest against excessive API fees, but many other subreddits are; check out the progress among subreddits that pledged to go dark on 12 July 2023 and the top 255 subreddits (even those that never joined the protest).

Think /r/math is too advanced?

This is a subreddit for learning math, and can be seen as a sister subreddit to /r/math. Post all your math-learning resources here. Questions, no matter how basic, will be answered (to the best ability of the online subscribers).

**Follow reddiquette. Be civil and polite; this is meant to be an approachable community for discussion of reason and logic.**

*EX:* [High School Math] Quadratic Equations

*EX:* [University Statistics] Probability

• Include instructor prompts (if any). What does your instructor (or the text) want you to accomplish?

• Tell us what is holding you up. Where are you in the process? Provide those who help with as much information as possible.

• Include any equations or assumptions you are using, and descriptions of any attempts you have made.

- We recommend using Imgur to upload images for linking inside posts.
- Reddit Enhancement Suite allows Imgur URLs to be expanded inline but doesn't work so well for other image-hosts.

ChatGPT and other large language models are not designed for calculation and will frequently be /r/confidentlyincorrect in answering questions about mathematics; even if you subscribe to ChatGPT Plus and use its Wolfram|Alpha plugin, it's much better to go to Wolfram|Alpha directly.

Even for more conceptual questions that don't require calculation, LLMs can lead you astray; they can also give you good ideas to investigate further, but you should *never* trust what an LLM tells you.

• "Do this for me" posts

• personal information (Check your documents before posting.)

• offers or solicitations of payment in any form

• surveys (Take them to /r/samplesize.)

• advertisements of any form

• posting of quizzes or lists of questions

• one-sentence posts (Have some respect for people who take time to answer your question and follow the posting rules.)

• image or video link-posts (Links to articles, Desmos, Wolfram|Alpha, and the like are fine.)

• being a jerk (Jerks get banned.)

Type this as an example (replace the `[-;`

with `[;`

when typing):

- `[-;e^{\pi i}+1=0;]`

You will see `[;e^{\pi i}+1=0;]`

formatted as in a textbook if the MathJax UserScript is installed and working.

• You will need to install a UserScript loader first.

- If your browser is so outdated or unusual that the linked advice doesn't work, consider these ideas.

**Best read with**

- /u/lewisje's list of math resources
- list of interactive math websites
- /r/math
- /r/askmath
- /r/cheatatmathhomework
- /r/academiceconomics
- /r/LearnEngineering
- /r/checkthis

**Other resources include**

- Khan Academy
- Brilliant
- Alcumus
- CTY Online AP & College Math
- ODE videos on YouTube
- /r/tutor
- Compilation of Free online math resources
- /r/bibliographies
- Prepform
- World Mental Calculation
- /r/STEM_Study_Groups/

Basic Math Symbols

≠ ± ∓ ÷ × · − √ ‰ ⊗ ⊕ ⊖ ⊘ ⊙ ≤ ≥ ≦ ≧ ≨ ≩ ≺ ≻ ≼ ≽ ⊏ ⊐ ⊑ ⊒ ² ³ °

Geometry Symbols

∠ ∟ ° ≅ ~ ∥ ⟂ ⫛

Algebra Symbols

≡ ≜ ≈ ∝ ∞ ≪ ≫ ⌊⌋ ⌈⌉ ∘ ∏ ∐ ∑ ∧ ∨ ∩ ∪ ⨀ ⊕ ⊗ 𝖕 𝖖 𝖗 ⊲ ⊳

Set Theory Symbols

∅ ∖ ∁ ↦ ↣ ∩ ∪ ⊆ ⊂ ⊄ ⊊ ⊇ ⊃ ⊅ ⊋ ⊖ ∈ ∉ ∋ ∌ ℕ ℤ ℚ ℝ ℂ ℵ ℶ ℷ ℸ 𝓟

Logic Symbols

¬ ∨ ∧ ⊕ → ← ⇒ ⇐ ⇔ ∀ ∃ ∄ ∴ ∵ ⊤ ⊥ ⊢ ⊨ ⫤ ⊣

Calculus and Analysis Symbols

∫ ∬ ∭ ∮ ∯ ∰ ∇ ∆ δ ∂ Δ δ ε ∂ ‖ ℱ ℒ ℓ

Mathematical Greek Letters

𝛢𝛼 𝛣𝛽 𝛤𝛾 𝛥𝛿 𝛦𝜀𝜖 𝛧𝜁 𝛨𝜂 𝛩𝜃𝜗 𝛪𝜄 𝛫𝜅 𝛬𝜆 𝛭𝜇 𝛮𝜈 𝛯𝜉 𝛰𝜊 𝛱𝜋 𝛲𝜌 𝛴𝜎 𝛵𝜏 𝛶𝜐 𝛷𝜙𝜑 𝛸𝜒 𝛹𝜓 𝛺𝜔

/r/learnmath

1

Hey. I am trying to recreate a serrated leaf pattern with math, as seen in the image below. I am using the desmos website, could someone smarter than me help me out? Tnks.

https://imgur.com/jVqRVEy

0 Comments

2024/06/30

13:56 UTC

13:56 UTC

1

I need to learn Linear Algebra, Calculus, Probability and Statistics, Discrete maths. I want to know these subjects in depth (well not too much)

1 Comment

2024/06/30

13:42 UTC

13:42 UTC

5

Different people have different opinions on what would be the correct reading material to continue. For reference, I just finished Stewart's precalculus and according to most people Stewart's calculus books are the way to go only for computational calculus. Many people also mention Spivak's calculus, at the same time I saw quite some people say that it's something to read with calculus background. So, what do I do?

6 Comments

2024/06/30

12:15 UTC

12:15 UTC

2

Hi guys,

Most Linear system theory books assume mathematical maturity, but I was looking for a book that assumes zero mathematical maturity and kills two birds with one stone by teaching/developing proof writing skills while teaching Linear Systems Theory. Does such a book exist? If there is none for linear system theory, such type of book for mathematical optimization or graph theory would also work for me.

Cheers

0 Comments

2024/06/30

11:03 UTC

11:03 UTC

1

Hi guys, I just tried to prove the trigonometric subtraction formula on my own, but other than for the addition formula the scheme I am using turns out to be a bit tricky. Maybe someone can help me find the error in my proof, as I was already trying it for the third time and it just did not work out...

Thanks in advance, any help is highly appreciated!!

Have a great sunday

4 Comments

2024/06/30

10:42 UTC

10:42 UTC

1

I'm an incoming college student and I find it hard to get worksheets through the internet. Any tips or suggestions on where I can get one? (Specifically College Algebra, Pre-Calculus, Calculus 1, and Calculus 2)

0 Comments

2024/06/30

10:18 UTC

10:18 UTC

1

Some of the 80960 lattice points in a 40 by 2024 lattice are coloured red. it is known that no four red lattice points are the vertices of a rectangle with sides parallel to the axes of the lattice. What is the maximum possible of red points in the lattice?

0 Comments

2024/06/30

08:53 UTC

08:53 UTC

1

I'm studying Complex Analysis next semester, but there is no recommended textbooks for the class. I enjoy using textbooks as supplementary material, and am looking for recommendations.

The only prerequisite is Real Analysis, and the topics of the class includes: topology of the complex plane, convergence of complex sequences and series, holomorphic functions, Cauchy-Riemann equations, harmonic functions and applications, contour integrals, Cauchy Integral Theorem, singularities, Laurent Series, Residue Theorem, evaluating integrals with contour integration, conformal mapping, and the Gamma Functions.

If anyone has any recommendations of textbooks for this material it would be greatly appreciated!

3 Comments

2024/06/30

08:52 UTC

08:52 UTC

2

so i was averaging 22/25 on the amc 8's and decided i could move on to mocking amc 10s. i got 84, and i dont really know what to do from here. i've been doing aops volume 1 and alcumus. is there anything else i can do? my goal is making usajmo or usamo.

1 Comment

2024/06/30

07:49 UTC

07:49 UTC

2

How to find the **exact** value of x if : 3ˣ - 2ˣ = 64? I tried solving it but no logarithms or exponential laws helped me. Any hints?

5 Comments

2024/06/30

05:51 UTC

05:51 UTC

2

So i completely bombed my midterm for my Integeral Calculus course, i got a 24%. My current mark in the course is 59% (with the assignments we do). The class average for the first midterm is 40%

Idk why, but i have so much motivation to improve for my next midterm and final exam. I want to learn the content truthfully and I want to do well. The topics are not bad and I could truthfully admit that I did not ‘practice’ enough as I wanted to for the first midterm.

There’s still a lot idk know on how to study in university as I’m a first year, I’m wondering if anyone has any tips on how study smarter with learning math? There’s so many practice questions and practicing takes time.

I have my second midterm in 24 days from now

My plan is going back to understand the content of the first midterm where I can perform majority of first midterm correctly and be able to answer most questions as these are the foundations for the next topic, and then jumping in to comprehend the second midterm topics as well as doing as much practice questions as I can from the textbook.

How do I go about learning the topic and doing practice questions? Any tips? Should i be attempting to do as many practice questions as I can, or should I select a certain amount and do them over and over again until I get it perfectly. Or is there a better way? Are there any resources anyone could recommend?

2 Comments

2024/06/30

05:49 UTC

05:49 UTC

5

A rock is thrown straight up into the air from a height of 4 feet. The height of the rock above the ground in feet, seconds after it is thrown is given by

-16 t**^(2)**+ 56t + 4.

For how many seconds will the height of the rock be at least 28 feet above the ground?

If "at least" includes equals, 3 is correct.

28 = (-16)(3^2) + 56(3)+4

Becomes

0 = (-16)(3^2) + 56(3)+4 - 28

Becomes

0 = (-16)(3^2) + 56(3) - 24

0 = (-16*9) + (56*3) - 24

0 = (-144) + (168) - 24

0 = 168 - 144 - 24 = 24 - 24 = 0 ✅

Source: Modern States CLEP College Algebra, Module 2.2, Question 3

**Answer options were 0.5, 1.5, 2.5, 3.0, and 3.5**

It says correct answer is 2.5. Shouldn't it be 3?

26 Comments

2024/06/30

05:28 UTC

05:28 UTC

3

thare is a picture of a suitcase, it dimensions are 22×35×50 cm, and i need to guess how much kinder bueno bars there are inside. based on calculations and your guess, what number would you send?

1 Comment

2024/06/30

05:24 UTC

05:24 UTC

2

Hello, I need a tutor for this course as it’s entirely online so I can receive help on tests and other things. We can meet on zoom and I would like to meet at least 3 days in the week. Msg me ur rates.

2 Comments

2024/06/30

04:16 UTC

04:16 UTC

2

6 Comments

2024/06/30

02:10 UTC

02:10 UTC

6

```
Good afternoon, I was reading a book and it mentions that this statement is false. My question is why, Sorry for my english btw
∃x∀y (x ≥ y),
```

14 Comments

2024/06/30

01:21 UTC

01:21 UTC

1

picture of my work here essentially i’m trying to find the partial derivative with respect to y of f(x,y)= 2x^3y my first method i ln both sides then d/dy both sides, multiply f(x,y) to the right side and replace it with the function. my second method i do e^ln of the right side.if the ‘x’ didn’t have a coefficient then method 1 works. but since it has a coefficient of 2 method 1 stops working but WHY. if you are confused by my explanation just click on the imgur link to see both methods.

5 Comments

2024/06/30

01:20 UTC

01:20 UTC

4

Long story short: I'm taking Calc 1 next semester in September. I did well in Pre-Calc and Calc in high school, but panic-withdrew from Calc 1 early on on my first try because I realized I had forgotten natural logarithms (and also because of unrelated personal circumstances). My prerequisites expired this month, but a student advisor took pity on me and gave me a one-time-only exemption, so I really really don't want to do this course any less than perfectly. I've been reviewing Calc 12 and it's been going pretty well, I think I just needed to jog my memory. I was thinking that in an ideal world, having looked over every topic on the course outline, I could walk into class on the first day already having at least some base-level understanding of most of the concepts

4 Comments

2024/06/30

01:20 UTC

01:20 UTC

1

The question was

2.25y-12=0.25y-4

Here’s my work:

2.25y-2.25y-12=2.25y-0.25y-4

-12=2y-4

4+-12=2y-4+4

-8=2y

y=-4

I entered -4 and it turns out the answer was just 4. I dont understand what I did wrong in my work.

3 Comments

2024/06/30

00:50 UTC

00:50 UTC

1

My husband and I are arguing about a math problem.

He said if we get a 3rd cat, it will be 50% more poop we have to clean. I can't wrap my head around why it would be 50% more poop to clean and not 33% more.

Could someone explain why it's 50%? Math isn't my strong suit..

9 Comments

2024/06/30

00:21 UTC

00:21 UTC

3

I am currently studying precalc with the usage of the Stewart precalc book. When doing the exercises should i by doing the proofs. For instane prove that the triangle inequality is true for all real numbers x and y. I mean i get why but i dont know how to do a formal proof? Is that really expected in precalc. I can do all of the exercises revolving applications, skills and concepts.

8 Comments

2024/06/29

22:51 UTC

22:51 UTC

2

Excuse the imprecise title. Here is what I'm talking about.

In How to Prove it, one of the exercises asks me to analyze the logical form of the following statement:

x ∈ ⋃F ∖ ⋃G

this means x ∈ U F and x not ∈ U G

so ∀x(∃i∈I(x∈A_i) AND ∀i∈I(x is not an element of A_i))

This is the first place I arrived. But my issue with this is that it uses A_i twice, but shouldnt it specify a different set, considering as it stands now it is directly stating a contradiction?

One way to remedy this would be to select a new index j for the RHS of the conjunction.

∀x(∃i∈I(x∈A_i) AND ∀j∈J(x is not an element of A_j))

But again, the 2nd instance of the set A is confusing to me. It makes more sense to me to say

∀x(∃i∈I(x∈A_i) AND ∀j∈J(x is not an element of B_j))

However, the solution I found online, which matches the simplicity of the solutions from earlier exercises (that I also over complicated by using indexed families instead of ??regular?? families) is:

∃A∈F(x∈A) and ∀A∈G(x∈/A)

And again, I recognize that this is saying the same thing but without specifying indexes. But it also reuses the set A.

So here is the gist of what I'm confused about:

***(1)* Why reuse the set A?** This is similar to an issue I had with a different exercise that said:

{n^2 + n + 1 | n ∈ N} is a subset of {2n+1 | n ∈ N}

Which also greatly confused me because it reuses n, but the actual solution ended up using a different natural number m to establish the equality n^2 + n + 1 = 2m+1

Which definitely makes more sense to me. So why not just START OUT with the second variable in the initial statement??

***(2)* How am I supposed to know when I should be using indexes for a question about a family?** IIRC, the book directly defines families using indexes. So where are the indexes in the simple solutions? I am repeatedly "overcomplicating" my solutions and its leading to unnecessary confusion. Sometimes the book specifies some family F, and the solution ends up using indexes. But in this example and in others, a different family simply denoted as F doesn't use indexes. ??????

Apologies for such a long post. Thank you

5 Comments

2024/06/29

22:40 UTC

22:40 UTC

0

Why does the exponent of c disappear when combing like terms?

C^2 = a^2 + (2a^2) C= 3a^2

4 Comments

2024/06/29

22:30 UTC

22:30 UTC

2

I can't seem to grasp the idea of how, with more dimensions, the data points become sparse, yet I have in mind the argument that given a hypersphere, as the number of dimensions increases, almost all the volume is near the surface area of the hypersphere. Intuitively, this makes it seem like they should be "dense."

2 Comments

2024/06/29

21:59 UTC

21:59 UTC

1

-3/4x^3y (1/2xyz^4) (-xz^5) I simplified to -3/8 -x^5 y^2 z^9 But apparently the whole thing should be positive. Isn't -3/4 (1/2) = -3/8? Same with x(x)(x)(x)(-x)?

5 Comments

2024/06/29

21:09 UTC

21:09 UTC

5

Hi everyone,

I’m on a journey to self-study algebra, starting from the basics and aiming to reach a graduate-level understanding. I have some questions about the best resources and approach for this journey, and I would love your advice.

I've been working through *Gallian's "Contemporary Abstract Algebra"*, and I find it quite enjoyable and accessible. However, I've seen some comments calling it a "middle school level" book. Is it still a good resource for someone at the beginning of their algebra studies? Should I stick with it or consider another book?

I've heard about *Dummit and Foote's "Abstract Algebra"* as a popular undergraduate textbook. Are there other books that might be better for an undergraduate level? How does *Dummit and Foote* compare to *Gallian*?

For graduate-level algebra, I’m aware of several options but I'm uncertain about which are best for self-study:

- Is
*Serge Lang's "Algebra"*a good choice for someone studying on their own? I've read mixed reviews regarding its suitability. - Should I also consider other graduate-level books like
*Rotman*or*Hungerford*? And do I really need to read both of Hungerford’s books (the undergraduate and graduate ones)?

Is it necessary to use separate books for undergraduate and graduate levels, or is there a single book that can cover both adequately?

Any recommendations for a coherent study plan or sequence of topics/books would be greatly appreciated!

Thanks in advance for your help!

1 Comment

2024/06/29

19:39 UTC

19:39 UTC

1

Hello, I am very concerned about my class. I am taking a summer precalculus class and I am struggling alot. In the spring I got a high A in my intro college math course so I was fairly confident I could handle this summer program, but it just feels like too much.

I absolutely love math, but I feel overwhelmed as we are taking tests every single week and we often go into the next unit before the previous unit's test is due which leads to information overload. I have done pretty good on the past two tests with an 85 on the first and 99 on the previous test, but I just took my third test which involved logarithms, inverses, and finance formulas and I struggled a lot on it.

I feel like the course is going too fast. I am studying 20 hours a week minimum and its still a lot due to how fast the program is going. I have been able to retain a lot of the info, but often the info I previously learned escapes my brain at the worst of times. I am going into physics, so I have to take this course and do well to feel confident I can handle this. I have until July 3rd to drop the course. I actually got accepted to university to transfer to this fall, so I was considering dropping this course and taking it in the fall at my university.

I believe my university offers infusion classes where you take calc 1 and precalc at the same time, but the concepts are taught in separate classes as they have calculus 1A infused with precalc then calculus 1B infused with precalc and so on and so forth.

I just feel extremely overwhelmed currently due to how much is being thrown at me. We actually just started trig this past week and it has been a lot of info to take in despite loving it. I really enjoy the course and the instructor is good, but its just a lot to deal with. I am also worried I could get a C or even a D in the course despite how I have been doing on homework and tests overall. It just feels like one bad test could ruin it all and I know I will have to get used to this due to my major, but its just a lot to take in. Maybe I just need some motivation to keep going. I am not sure.

Any advice is appreciated,

Thank you

5 Comments

2024/06/29

19:21 UTC

19:21 UTC

0

Why is that we can find the values of f(x)= root(x), like root(101) using dy/dx, On trying the same with f(x)= Logx or k^x {k being a any integer}, i dont get what i would find on a calculator. If there is way to find values such as 10^1.6 without using expansion( its not possible to do expansion during a exam :p) can you mention

14 Comments

2024/06/29

19:17 UTC

19:17 UTC

52

For some context, I have a bachelors in physics and a masters in computer engineering. I miss learning things so I picked up a deep learning textbook that a professor recommended in grad school - which is essentially all math. To be completely honest, I forgot a lot of the content. I dont remember many of the terms of the book, some yes but still not enough.

Even in school I would avoid textbooks because they would just confuse me even more. Now that I dont have a professor with me I think textbooks are the only way i can reinforce fundamentals and learn new things - but they seem impossible to read. The one I want to read is +600 pages of dense material.

16 Comments

2024/06/29

19:08 UTC

19:08 UTC

1

Hello everyone so I graduated hs doing ab calc and afterwards joined the military and took a break a year after I got out and I’m now going back to school. This summer, because I have so much time, I wanna reteach myself calculus. I have been watching a ton of videos but I really want something more structured either videos or books if anyone can help me out.

1 Comment

2024/06/29

18:30 UTC

18:30 UTC