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

Hi, I'm currently doing a ECE bachelor after switching from CS and maths classes are tough. So tough in fact, I can't rely on the lectures alone. I have trouble with integrals.
I am looking for books containing training exercises about integration.
Thank you

I feel answer could be 111 after solving LHS and RHS. Still confused

Update: thanks for the answers. I'm hereby closing the doubt.

Would you say math/physics teachers or engineers in industry do more calcs by hand? Trying to choose a career path that suits my passion for the subject matter...

I understood what's asked and I can draw a mental model of the answer but I want a mathematical proof why this works ?

I am in 11th rn in India and I am 17 for the past 2 years I never picked up book failed 2 times in maths got low grades (The only thing I hate is that my brain didn't develop in those 2 years I lost that time) This year I wanted change and I started studying and I might complete grade 11th maths this month check the whole syllabus below.

Ch 1 -> Sets

Ch 2 -> Relations and Functions

Ch 3 -> Trigonometric Functions

Ch 4 -> Complex Numbers and Quadratic Equations

Ch 5 -> Linear Inequalities

Ch 6 -> Permutations and Combinations

Ch 7 -> Binomial Theorem

Ch 8 -> Sequences and Series

Ch 9 -> Straight Lines

Ch 10 -> Conic Sections

Ch 11 -> Introduction to Three Dimensional Geometry

Ch 12 -> Limits and Derivatives

Ch 13 -> Statistics

Ch 14 -> Probability

I wouldn't say it was easy even some basics ate my head.

After this I would do class 12th maths but what after that?

Which is better ?

I’m a B.Sc. Mathematics & Computer Science student and I’m currently deciding between M.Sc. Mathematics at Babasaheb Bhimrao Ambedkar University (BBAU) and Lucknow University (LU).

I’m from Lucknow, so both are possible options for me. I want to know the actual ground reality rather than just comparing rankings.

For students/alumni who have studied M.Sc. Mathematics at BBAU or LU:

• How are the professors and teaching quality?
• How difficult/strict is the department?
• Is the syllabus manageable and are 70%+ marks realistically achievable with regular study?
• How are exams and evaluation? Is the checking very strict?
• What is the attendance requirement and overall academic pressure?
• How is the environment and student culture?
• Are there good opportunities for research, NET/JAM/GATE preparation, internships etc.?
• How useful is the degree for PhD or jobs after M.Sc.?
• Most importantly, if you had to choose again between BBAU and LU for M.Sc. Mathematics, which one would you choose and why?

Please give honest opinions based on your own recent experience, especially students from the last 2–3 years. I’m not looking for promotional answers or just university rankings.

I know the most common method to calculate groups of 3 is A * (A-1) * (A-2) / 3! and the method for groups of 4 is A * (A-1) * (A-2) * (A-3) / 4! but here I have alternate methods:

An alternate method is using the groups of 2

There are 6 groups of 2 with 4 objects and the groups of 2 appear twice when listing the groups of 3. You have to multiply the number of groups of 2 by the times they appear and divide it by 3

6 * 2 / 3 = 4

There are 4 groups of 3 with 4 objects

However it actually gets trickier when you use groups of 2 with more 4 objects. There you have to multiply each group of 2 by the times they appear and then divide it by 6 (because 6 is the number of possible groups of 2 with 4 objects). For example there are 10 groups of 2 with 5 objects and the groups of 2 appear 3 times there

10 * 2 / 6 = 5

There are 5 groups of 4 with 5 objects

Another alternate method is using the groups of 3

There are 10 groups of 3 with 5 objects and each object appears twice in the groups of 4

10 * 2 / 4 = 5

There are 5 groups of 4 with 5 object

I think you already got it

In arabic or in japanese for exemple, how do you name variables ? How do you use the notation dy/dx ? Does it make sens for you to use se sigma for the sum ?

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Its this book.

I would like to rank different members. Each member has varying numbers of submissions

In a list of 1000, #1 has gets 1000 points, #2, gets 999, and so on.

But I don’t want to give a member an advantage if they have many more submissions than another.

How do I weigh it so that every member has the same number of points to earn, in the kind of points system outlined above?

So unfortantly I grew up in some insane cult where they don't teach you anything non-religious, including math.

Just left the cult a few months ago (currently 19)

My actual passion is science and specific astrophysics, a career which lives on math daily.

I'm a very intelligent person and a very good student, I just really have zero knowledge about math

Any online course / youtube channel for people without learning disabillities teaching everything from the beginning?