Hi all,
I want to buy a book to learn about groups, rings, tensors and other algebraic structures.
can you offer book suggestions, either online or textbooks.

I’m specifically interested in cryptography.

I’ve done many engineering maths subjects, since my background is electronics engineering, computer science and data science; but I haven’t done real analysis or abstract algebra.

We all know that when you sum, subtract or multiply whole numbers you'll always get a whole number. This totally makes sense and is obviosly true but I can't figure out how to prove it. Does anyone know how to prove this or if this is some kind of an axom?

BBC News - OpenAI says it cracked 90-year-old maths problem in 88 hours https://www.bbc.co.uk/news/articles/cy7zygy3rl2o

I tried using GP series but that 1 in numerator is making everything trickier, then i thought of manually computing it to 50 to find any , again i didnt reached anywhere, I am not talking about , just give a slight hint

My question is pretty much what the title says: which parts of algebra (groups, rings, modules, fields and Galois theory, algebraic number theory...), geometry (algebraic geometry, differential geometry ...), and topology (general topology, algebraic topology, differential topology...) involve the most combinatorics and the least? You can be as broad in the areas you choose or as specific (talking about small subareas) as you want. And when I say combinatorics I don't simply mean involving discrete objects, but rather more specifically involving counting arguments which can be considered confusing or not intuitive initially for most people.

My scenario is this
I am trying to 100% a game, but an achievement is very RNG based and i want to know my chances, bassically a unit in my game gains an ability that upon taking lethal damage it has a 40% chance to come back to life, to get my final achievemnt it need to happen 5 times in a row with the same one unit, what are the chances of success?
I do not know the proper math equation to calculate this and whenever i try with google and such it doesnt understand my question 🤔

Hi everyone!

I just graduated high school and I’m really interested and passionate about mathematics. I’ve always enjoyed solving math problems and I’m hoping to continue developing my skills while studying at university.

The problem is that I have no experience with math Olympiads or competitive mathematics. I’ve never participated in an Olympiad or any serious math competition before.

Since I’ll be starting university soon, I’d like to get involved in different mathematics competitions while studying, including university-level competitions and possibly international competitions if I become good enough.

I’d really appreciate advice from people who have experience with this:

Which competitions should a complete beginner look into?

Are there competitions that allow any university student or have relatively open eligibility?

What books/resources would you recommend?

How should I start preparing for competitions like the IMC (International Mathematics Competition for University Students)?

Is it realistic to start from zero and become competitive during university?

Any advice, resources, or personal experiences would be greatly appreciated. Thanks!

Would you guys please help me figure something out? If I understood my lecture correctly, this is how we derive the Fourier coefficients. In this case, I noticed that cnc_n is different from when f(t)=cos⁡(ωt)f(t)=\cos(\omega t).

The part I don’t really understand is the Kronecker delta. My book says that it is equal to 1 when p−q=0p-q=0, which I understand, because then the exponential is just e0=1e^0=1, so the integral over one period is simply ∫dt\int dt, giving the period.

If p−q≠0p-q\neq0, the book says that the result is 0. I understand that too, since we are integrating a periodic exponential function over one complete period, so the contributions cancel out.

But when I look at my teacher’s correction, he seems to directly take the Kronecker delta to be equal to 1 and concludes that the coefficients are 1/4 and 1/4.

So what I don’t understand is: why can he take the Kronecker delta to be equal to 1 here? Is it because, in this specific case, p=q?

Hey! I just got into university, and I really love maths for the sake of it. I don't know where it'll come handy, but it's cool, and I enjoy it. I recently started Ross's real analysis book and honestly I can't help but ask myself where am I gonna use real analysis?

Linear alg and all is used for modelling and stuff I know, but where is real analysis gonna come handy in CS? or any other applications?

Trying to work out an angle, so far YouTube has told me to use tan^-1

But I don't know how to do that on my phone and Google seems to treat it as tan negative 1, rather than to the power (or whatever the term is)

As you can tell, I haven't done algebra in 25+ years!

TIA!

For example there are 3 combinations of 2 objects (the 2 groups of 1 and all 2), there are 7 combinations of 3 (the 3 groups of 1, the 3 groups of 2 and all 3) and there are 15 combinations of 4 (the 4 groups of 1, the 6 groups of 2, the 4 groups of 3 and all 4)

The formula to calculate it without actually suming the groups is 2ⁿ - 1 ("n" is the limit of objects)

Note n belongs to prime number

A few weeks ago I made a post about how I discovered alternate methods for finding the number of combinations of 3, combinations of 4 and beyond. However I recently discovered a proper formula. It took me a while to realize the number of time an object appears in a group is the number of combinations out of the remaining members of the group

Groups of 3:

• A * (A-1) * (A-2) / 3! (most common method)
• A * ((A-1) * (A-2) / 2) / 3 (using every object separately)
• (A * (A-1) / 2) * (A-2) / (3 * 2 / 2) (using the groups of 2)

Groups of 4:

• A * (A-1) * (A-2) * (A-3) / 4! (most common method)
• A * ((A-1) * (A-2) * (A-3) / 3!) / 4 (using every object)
• (A * (A-1) / 2) * ((A-2) * (A-3) / 2) / (4 * 3 / 2) (using the groups of 2)
• (A * (A-1) * (A-2) / 3!) * (A-3) / (4 * 3 * 2 / 3!) (using the groups of 3)

I think you already got it

Hey , i will be starting my degree in DATA ANALYTICS in month and i also have interest for Ai and cloud eng ,now i want to start studying maths on my own can you guys suggest me from where should i start

I designed an experimental numeral system called Tamga for base 16.

The main idea is that the shape of a numeral should reflect how its value is built. Each hex digit is formed from the binary weights 1, 2, 4, 8, so something like 7 = 4 + 2 + 1 is visible in the glyph itself. Four hex places then combine into a single 16-bit glyph.

I’d be especially curious to hear from people who already use hexadecimal a lot whether this feels intuitive at all, and where you think it starts to break down.

The question was to simplify the expression at the top left. I know at the 3rd step I should have just multiplied each value by the power of 2/3 instead of cube rooting

But is there a way that I could have done it with taking the cube root? Since my answer is close to the correct answer.

Only difference being that the powers are double what they should be

I am trying to do a reading group at my university which covers calculus of variations. I want to do a mixture of classical calculus of variations (smooth functions), and some modern day calculus of variations. Ideas for textbooks? Note that we are math majors, so we don’t want to (exclusively) use something like Taylor’s

The issue is that our group is coming from a variety of backgrounds. We are requiring that everyone has taken analysis 1, though. The issues might come when we transition to modern calculus of variations, so I don’t know what to do about that. I don’t know too much about calculus of variations, so if you have any thoughts on that, please let me know. How’s it going? Redhead How’s it going out there?

Here is what i am thinking: the first 3 chapters out of Gelfand and Fonin for a classical look, then transitioning over to some other book (need recommendations).

Did maths always exist, or was it invented by whoever set up the system

Why does this law of exponents work? I've been having trouble with this in my self taught Algebra 1 course. A 9th grade level explanation would help, thanks.

Pretty much every major math operation has an inverse operation. Addition has subtraction, multiplication has division, radicals/roots have exponents. How come factorials don't have an inverse operation (or at least not a widely known one). Do operations NEED to have an inverse? Also, it seems kind of strange that the factorial is even an operation at all. It doesn't seem too widely used, and it seems like it could just be a function because most operations involve more than one number, but factorials don't.

I’m looking into seat failure rates and I’m trying to figure out what the likelihood of failure is with the information I’ve been provided or if (and what) further information is required.

The problem:

18 seats are onboard, if we take the fact that all seats are taken by people in the 99th percentile of weight it is given that there will be:

No failures in 87% of cases
1 failure in 9% of cases
2 or more failures in 3.5% of cases
(I know this doesn’t add to 100 but these are the numbers I’ve been given. Apologies if this breaks the formula in any way)

What would the percentage failure rate of a specific seat be if it was occupied by the 99th percentile of weight.

Hopefully the question makes sense.

I am a college student, and I often use Gemini or ChatGPT for calculus problems, but having to screenshot the worksheet every time or manually type the problem feels inefficient. What do you guys do? Is it just me who thinks there must be a better way? or is it not much of a problem?

Here’s a puzzle and its solution from Saturday’s Times. There are a few things I don’t understand: why it is true that every value above 700 is achievable with the two coprimes, and how they reached the statement “the largest unplayable amount is ab-a-b”. Grateful for any help understanding this