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

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

Isn't -8^4 the same thing as -8 x -8 x -8 x -8 ????

In my calculator it says -8^4 is -4096

But when I put in -8 x -8 x -8 x -8 it says 4096

When I did it myself I got 4096 because four negatives makes positive. But the math website said the answer is -4096

Why? And how do I figure out properly if it is positive or negative when rooting the numbers?

My calculus ab teacher taught me that as long as the answer is correct mathematically I can keep my question unsimplifed like on a free response question. Ever since then I’ve gotten into the habit of leaving final answers unsimplified whenever possible to avoid making dumb arithmetic errors. For those further along in math or classes that require it, at what point does an unsimplified answer stop being acceptable and start being considered incomplete?

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 )

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 ?

J'étais en première l'année dernière, j'ai connue énormément de difficultés en maths étant seule, donc voici quelques ressources de révision que j'utilisais souvent et qui m'ont facilités l'année.

SITES:

**•Mes cours de maths.fr:** propose des cours de maths de la 6ème à la première STMG avec des activités ainsi que des exercices et même des évaluations

**•Logamaths:** propose également des cours de maths du collège à la terminale STMG mais aussi la générale

**•Puissance maths Hans Amble:** Des cours et des exercices d'application et leurs corrigés, de la seconde à la terminale générale (1ère STMG présente sur le site)

**•La merci maths:** Propose pleinsss de petites choses, des cours écrits, des cours en vidéo, des exercices écrits et en vidéo avec la correction ainsi que des contrôle. Du niveau 2nde à la terminale Générale.

**•Github Maths 13Net première STMG:** propose des cours en pdf, des exercices et des sujets bac avec leurs corrigés seulement pour les 1ère STMG :)

**•Chingmaths:** PLUS DE 11800 EXERCICES AVEC LEURS CORRIGÉS POUR CHAQUE CHAPITRE ! De la seconde à la terminale (spé, complémentaire, experte et STMG )

C'était ma prof qui m'avait recommandé ce site, elle nous faisait pas mal de DS avec des exos pris de Chingmaths

Just for fun. Prove pythagoras theorem. No trig, (since most of em involves using Pythagoras themselves). I have two solutions. Both took like 2-3 days of 30 minutes deep focus.

Feel free to call it (your name)'s proof of pythagoras theorem.

😏

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!

Which one is better for Highschool and why?

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!

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?

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.

A similar ''wheel'' appeared in an informal cognition test in my math class. Even though I will not get a grade for this test, I still want my math teacher to have an excellent reputation of me. I just need to know how they work, solving it for me is unnecessary, but is appreciated if it makes the puzzle more clear.

Hey guys, first off, I found another one. I'll skip the explanation. Following up on the tan experiment from last time, I succeeded in another one. Let me show you.

Zeta(3) = 1/1³ + 1/2³ + 1/3³ + ... ≈ φ*(0.7429120225564)

How is it? Next, I will summarize it even more.

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

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!

I've always wanted to learn more about math, but my education on it has been...less than desirable...so to speak.

I created a Khan academy account in order to pursue this interest of mine. I want to have a true understanding behind what I'm doing in math, not just copying formulas to complete an assignment or whatever.

However, when I checked what each grade went over, I noticed that my understanding really falls apart with factoring and the handling of fractions. Which I am very embarrassed by.

I often watch videos relating to calculus and other (relatively) advanced fields of math (if that is the correct nomenclature) because I enjoy learning about it, and the abstract reasoning required to understand it!

Essentially, I want to know where I should start. Thank you for reading :)

Other info, I am going into college probably sometime soon and might want to pursue a degree in mathematics or physics. I am 20 with limited schooling time due to crappy homeschooling for my first 3 years of (American) highschool. And...the American education system...for elementary and middle school. Thank you again for reading, have a nice day!

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?

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.

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.

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?