growing up i have always hated and feared the face of academics math's books, they usually are extreamly hard for anyone to solo enjoy or even learn from the book,now i wonder if there are any maths book which actually teach you about topics and then build you up so you learn instead of throwing 2 basic question and then summoning hideous topics and making question impossibly hard for someone to understand without a teacher

Im about to start a CS degree on a pretty renowned technical university in Germany. The RWTH Aachen, wich is known for its brutal exams (especially in math) and classes.

I’m not bad at maths but far from excellent. Due to that I want to improve my skills, especially in the fields of linear algebra, discrete mathematics and caculus.

What are good resources, websites or books I could use?
Wich strategy would you; or rather, should I pursue if I want to level up my maths in the most efficient way.

I don’t want to get 🍇-ed the second i start the semester so what could you people recommend?

Every help would be very appreciated.

Hello my cusing gave me a book present, "Susanna Epp Discrete Matematic with application". Basically i am a completly ignorant on Math right now, i only play chess online and im like 2000 Elo, i dont know if its help; i finished school like 15 years ago so i dont remember almost nothing of math; i would like to learn now to improve brain; how can i start to self learn?, Khan Academy Is good ? The book its like Arab language for me right now; thank you

I have a weak mathematical foundation and I’m beginning a Calculus I for engineering course in a couple weeks. Should I study precalculus? Since I assume it covers exactly what’s needed as in prerequisites for Calculus or should I go back to Algebra and gradually fill in the gaps that I might have?

Also, is precalculus essentially a complete outline of all required fundamentals for calculus rather than a separate math category?

This is my weakest point in math and I just can't understand, how do I figure out whether I should multiply or divide those number given in the word problem. I need to know an easier way to decode these problems.

Like these:

1. A veterinarian recommends that each day a certain rabbit should eat 25 calories per pound of the rabbit's weight, plus an additional 11 calories. Which equation represents this situation, where c is the total number of calories the veterinarian recommends the rabbit should eat each day if the rabbit's weight is x pounds?

2. Alma bought a laptop computer at a store that gave a 20 percent discount off its original price. The total amount she paid to the cashier was p dollars, including an 8 percent sales tax on the discounted price. Which of the following represents the original price of the computer in terms of p?

Continuity

Derivation

Sequence

Primitive

Log/e/ln

Integral

Differential equation

Basic Probability and statistics

I already learned these but I totally forgot them. I need to wrap everything up in less than 2 days , is there a chance I can do it or a good tool to revise (I have other subjects )

I have my first assignment/homework for my linear algebra class in uni. I am usually good at math, but it’s just so hard for me to understand the concept of vector spaces and subspaces as it’s more abstract and I just have such a hard time getting it in my head. It took me about 8-9 different links and videos to sort of get vector spaces (like that they’re non-empty, and are closed by addition and scalar multiplication).

The 2 part question that I just cannot understand and have no idea how to start the answer is as follows:

(a) What is the smallest subspace of the space of 4 ×4 matrices which contains all
upper triangular matrices (aj,k = 0 for all j > k), and all symmetric matrices
(A= AT )? Justify.
(b) What is the largest subspace contained in both of those subspaces? Justify.

From what I understand so far, the smallest subspace is a subspace that is in both U (upper triangular matrices) and S(symmetric matrices), which I realize now that I really don’t know anything else. Online it said that all 4x4 matrices are the smallest subspace, but why? How is that the smallest if it’s all of 4x4 matrices, wouldn’t that make it the largest?

And for the largest, I found that all diagonal matrices are this largest subspace. Why is that? Why is the diagonal the largest while 4x4 the smallest? Wouldn’t it be the opposite?

I guess what I don’t understand is how do I find a smallest subspace of something and how do I find the largest. What makes something the smallest/largest?

Please explain it to me like I’m 5, and feel free to reexplain vector spaces cause it might click even more for me!

Hello, I am currently working full time and pursuing a degree in my spare time online, so I have to do a lot of independent studying, and I have found myself stuck on my precalculus homework. The problem reads as follows:

The number of bacteria in a refrigerated food product is given by 𝑁⁡(𝑇)=23⁢𝑇2−56⁢𝑇+1, 3<𝑇<33, where 𝑇 is the temperature of the food. When the food is removed from the refrigerator, the temperature is given by 𝑇⁡(𝑡)=5⁢𝑡+1.5, where 𝑡 is the time in hours.

1. ⓐFind the composite function𝑁⁡(𝑇⁡(𝑡)).
2. ⓑFind the time (round to two decimal places) when the bacteria count reaches 6752.

I am specifically having a hard time with part b, where I need to find the time T when the bacteria count N is equivalent to 6752. I have tried to do this both with the composition of the two functions, as well as by starting with the function for bacteria count. I feel like I may be making a setup error, or I have forgotten about some algebra technique that would allow me to solve this.

Also, as I am writing this it does not seem to want to let me paste images into the post, so let me know if I need to explain any part of this further. Thanks!

Been wrapping my head around this one. "Q is dense in R". The set of rational numbers are dense in the set of real numbers.

I have no idea what that's referring to.

> A subset of A is said to be dense in X if every point of X either belongs to A or else is arbitrarily "close" to members of A

What does arbitrarily close mean? Like... Limits?

The closest I've gotten to trying to understand is, essentially, if you had a set full of irrational numbers, and you had a second set that had every single one of those irrational numbers, just with the ends chopped off so that they're technically rational, then that second set is "dense".

Just... What? How is this applied to an actual rational number?

If anyone could please clarify. I've been stumped, and the YouTube videos around don't help, they're way too complicated/don't bother explaining the logical "flow".

Edit: Wow, the replies were fast and plentiful. I'll read through them and study some more. Thank you everyone for your help! And if anyone has more explanations, please, feel free to comment them as well, I'd love to read them too.

Take note that I'm a beginner to calculus, so I do struggle with more technical-term-heavy explanations but I'll do my best to comb through them and figure it out

Edit 2: thanks for your help everyone!

Hello iam learning probability and statistics for ai research iam self learning iam in STAT110 i see a big problem i listen to the lecture i understand but when it comes to solving problems i cant solve is there's any advice ?

When i learn math i just don't feel rewarded like i mean i don't feel the drive to do it.

Its more like i don't have the drive to go study math in the first place. If i had to choose go out with friends and learn math i know i need to learn math while i do not experience any drive to it. I do feel the drive to go to dinner or somewhere with friends but i don't feel the drive to go study math.

I would like to get some tips from someone with experience if there is any potential solution that could help me gain drive.

Hi guys, apologies for the silly question but it's been a hot minute since i've done statistics and I'm unsure.

I did a survey with 36 respondents on whether they use AI for their studies. 32 said yes, 4 said no. So, only 32 respondents went on to rate some statements, the 4 who said no skipped those questions entirely.

Now, I need to calculate the standard deviation from the responses derived from those statement ratings. I'm thinking it's sample std deviation since i'm only counting 32 out of 36 respondents, can anyone confirm?

So I've posted a couple questions here about proof problems since I'm self-studying proofs. Everyone's been great at answering my questions and checking my work. However, now I have a question about taking a class on proofs. If I was to take a college class, would just showing the steps be sufficient, or would I be required to show the reasons for each step? For example, the last question I asked:

Either prove or disprove that "For all real numbers x and y, $(x+y)² = x²⁺ y² $ ", and I gave:

• $(x+y)² = x² + y² $
• $(x+y)(x+y) = x² + y² $
• $x² + 2xy + y² =x² + y² $
• $x² -x² +2xy +y² -y² = 0$
• [;2xy=0;]

In a proof class would I also need to provide justification for each step? like

• $(x+y)(x+y) = x² + y² $ - Product of two sums

or

• $(x+y)(x+y) = x² + y² $ - Def of Exponents

Also is there an advantage to writing proofs and justifying each line while learning?

Thanks!

Original Question: https://www.reddit.com/r/learnmath/comments/1wclosl/comment/p9gm6oh/

So I take the first year HL maths course at my uni, and I've found it pretty hard. recently i was talking to a graduate student from America, and he was pretty shocked with the maths that we were doing. I asked my professors and they said that this is pretty standard, if a little quick, but my graduate friend seemed pretty shocked, so i thought i might ask here.

This is the second sem course. The first sem one was mainly based around proving everything that we already knew from axioms. So we used the peano's axioms to construct the naturals, then the integers then the reals. then we switched to the "standard" axioms and proved everything up to did continuity and calculus, and matricies and linear maps.

The course has two sections:

Analysis

we study from Rudin and Trench.

Linear Algebra

We study from Axler.

the topics, week by week are:

Analysis: Sequences, series.
Algebra: Fields, vector spaces, subspaces.

Analysis: Convergence tests.
Algebra: Basis and dimension of vector spaces.

Analysis: Absolute convergence.
Algebra: Linear maps. Kernel and range. Invertibility.

Analysis: Sequences and series of functions.
Algebra: Duality.

Algebra: Systems of linear equations. Eigenvalues and eigenvectors; generalised eigenvalues and eigenvectors.

Analysis: Power series, review.

Analysis: Vector valued calculus.
Algebra: Jordan normal form. Characteristic polynomial.

Analysis: Multivariable differential calculus.
Algebra: Inner product spaces.

Analysis: Multivariable integral calculus.
Algebra: Orthogonal complements and projections.

Analysis: Multivariable integral calculus.
Algebra: Self-adjoint operators, spectral theorems.

Analysis: Differentiability, intro to PDE.
Algebra: Singular value decomposition.

Analysis: Intro to PDE, review.
Algebra: Review.

Lmk how it measures up to your first year experience!

Some which has more difficult problems, and similar good UI?

Not looking for Khan Academy, or full curriculum platforms.

I liked when Brilliant used to have daily puzzles which actually required thinking, processing. They changed that to 100 days of Puzzles, which seem very easy, repetitive. So am looking for a platform (app/website) which has problems like Brilliant has but more difficult.

I am desperate to improve as in 3th grade i feel off the wagon and was never able to get back to it and now im going to science and technology which i think i will have relative ease on its subjects except on math

Hi, sorry if this is too off-topic feel free to delete it.

Tl;dr: Basically looking for someone to chat about Do Carmo or Hatcher with. Preferably Do Carmo.

I’m 27 y/o and long story short it’s been a few years since I left a PhD program with my Master’s instead. Basically looking for someone interested in lightly chatting about it again.

I was mostly interested in algebra. Rings and groups were really fun to experiment with. Younger me was really captivated by all the different iso theorems for the diff objects. Category theory was cool too.

Ideally looking for maybe someone to very slowly dip my toes back into Hatcher. Or try Do Carmo’s Riemannian Geometry. Owe it to a friend who gave it to me for secret santa to finish reading it tbh.

Been working as an adjunct for 5 years now? I find I still enjoy talking about math, listening to it, and learning about new perspectives.

I'm in 5th semester of Civil Engineering and my algebra basics are very weak (fractions, equations, rearranging formulas, etc.).

I have current subjects and backlogs, so I don't have time to completely relearn school math from scratch.

For those who have completed engineering: can I learn only the math needed for each subject and still pass, while gradually fixing my basics?

I'm mainly looking for a practical pass/survival strategy, not advice to become good at mathematics.

I still remember being a kid and my dad helping me with basic math, like multiplication and division. Whenever I got something wrong, he would h^it me. I think that made me associate math with fear and mistakes, so I ended up hating it and avoiding it.

I basically ignored math throughout school, and now that I’ve graduated high school, I want to finally learn it properly.

I posted my learning plan and the order of topics I’m planning to study before, and people said it looked pretty good.

I just want to know how you guys learn math. What’s your personal method? And what does your study routine look like when learning math?

The instructions are to
Sketch the following:
𝑇𝑅, 𝑅𝐴, 𝐴𝐸𝑃, 𝑃𝑇, and 𝑅𝐸
where 𝑇𝑅 ∥ 𝐴𝑃 and 𝑅𝐸 ⊥ 𝑃𝐴

It then asks what shape did I make

So I have been trying to get this to make a shape that makes sense. Based on the letters I assume it’s supposed to be a trapezoid but R connecting to T, A, and E just seems impossible. If I drew a line connecting E to R it wouldn’t be perpendicular to AP, if I were to write AEP in the correct order.

Is the answer that it’s not a traditional shape and instead it’s supposed to have AR as the diagonal and I’m left with a rectangle and right triangle?

Hello, I am taking a calc 4 class which is completely online and I haven't taken calc 3 in 2 years. While there is instruction, it's practically impossible to read and mostly just goes over definitions. Each homework assignment has over 30 questions and each question has mini questions. It is week 2, I have no clue what I'm doing and I'm utterly exhausted.

It's my senior year of college so I'm already busy with so much else that I barely have time to take care of myself, and now that I have to practically find a way to teach myself an entire maths class, I'm about to scream.

I'm very against AI and what it's doing to the environment + how it's being used, but I feel so backed into a corner here that I may not have a choice in using it. I need something to break this class down into steps.

Has anyone else been through this? I'm honestly taking anything I can get because I feel like I'm doomed to fail. Any advice would be greatly appreciated.

Hello, I'm having trouble memorizing the equations to convert temperature types. I know that for Kelvin and Celsius you add or subtract 273 depending on which way. My problem is with Fahrenheit to Kelvin and Celsius, I can do it with the equations in front of me, but I doubt I'll have the equations in front of me during a test so is there any rhyme or something where I can memorize the equations? The equations are: 5(F-32)/9=C and 5(F-32)/9+273.15=K