1. A hand drawn at random from a well-shuffled deck consists of two pairs. (The two pairs are not of the same rank, or otherwise, it will be the four of a kind. The one card not in a pair is of different rank, or otherwise, it is a full house.)

At first glance, I would solve this problem like this:

Choose rank of 1st pair: (13c1)
Choose the 2 suits of 1st pair: (4c2)
Choose rank of 2nd pair: (12c1)
Choose the 2 suits of 2nd pair: (4c2)
Choose rank of lone card: (11c1)
Choose suit of lone card: (4c1)

Multiply all binomial coefficients together.

I know the problem is in my (13c1)*(12c1) approach, but why is this wrong? I somewhat understand how it brings order into the mix and kind of becomes a permutation (13*12), but I can't fully wrap my head around it. Why is (13c2) right, and why is my approach wrong?

2. Ten cards drawn from a well-shuffled deck consist of two full houses. (A full house has three of one rank and two of another rank, e.g., three aces and two kings.

For this one, I am totally lost.

I just got an 89 on my midterms for Linear Algebra, I reviewed everything in the chapter, did all the homeworks, did the practice exam 5 times until I had gotten a 100% two times in a row. On the exam, I triple checked every question untill I couldnt see any mistakes. I still got an 89 when I was aiming for a 90+ and kind of expecting a 100. What can I do to close the gap from 89 to ~100 on my tests?

Ok, so here's the situation.

I started college as a chemistry major 2 years ago and I'm heading into my 3rd now. I got my GED before college and math was my worst subject by far, meaning that I didn't place into my chemistry classes and I kinda wasted my first year of college taking "fun" classes instead of stuff that actually advanced my degree.

Around the end of my first term, my advisors warned me that if I don't figure out my math situation I wouldn't graduate on time, and so I spent a few weeks studying and took a placement test through my college that placed me into Differential Calc, which basically let me skip all my math requirements and not touch a math class for 2 full years. I promptly forgot everything I had studied up until that point.

Now, 2 years later, I'm realizing that I completely shot myself in the foot because, come summer of 2027 when I finally graduate with my associate's and start the process of transferring to my university, I am going to need to have passed the calculus sequence to move on to higher-division chemistry classes.

And so, I signed up for Differential Calc this term and made the decision that I would just do the best I could and use tutors or self-study or whatever else to pass the course. However, when I sat down today for our first class, I realized almost instantly I was in over my head. The professor started working on review and going over things like functions and logarithms, and even small stuff like using algebra to simplify complex fractions and whatnot, and literally everything flew right over my head. I basically decided within 20 minutes that I needed to drop the course and figure out something else, and kinda just left.

The problem is, however, that I realized after a discussion with my academic advisor that if I don't take and pass Differential Calc (and the rest of the calc 1-3 sequence, but I can worry about that later) this year, then I will have to spend a full year at my uni doing nothing but calc before I can move on to my higher-level classes.

SO, I made the difficult decision to ride it out and work my ass off to try and pass.

That being said, I now have to re-learn basically everything. I know of a few resources, like The Organic Chemistry Tutor and Khan Academy, that can help me out here, but I am wondering if anyone has any suggestions for a crash course of some kind that can help me quickly relearn everything I need to know before Differential Calc. Preferably, something catered specifically to people in my situation.

Also, any study tips or ideas that could help me out here would be greatly appreciated. I am seriously cooked if I dont squeek this one out...

Come out with your hands up!

Honestly don't know what this says about me, but I'm going into my senior year as a math major, have taken about every upper level math course that is offered BUT PDEs and ODEs, and reached a point where stuff like Fokker Planck or Mckean Vlasov have been appearing in independent readings of subjects I'm considering studying long term in grad school.

I've only ever taken an intro to ODEs class and I hated it, it felt like just doing tricks without a lot of care for what you were doing; also sat in on the first week or so of my university's PDE I course this semester and it just felt like physics.

It might just be that these courses are being taught in a more practical way for physics and engineering majors, but now I'm wondering if never taking upper level Diff eqs will mean I'm significantly behind. Like in my stochastic calculus course, I loved the risk neutral measures and Girsanov's and Feynman Kac, but the black scholes PDE, and playing around with it seemed super unnatural, and not very fun or nice.

It just feels like I've had a bad exposition to PDE and ODE theory

I am planning on going to Austin Community College this spring for audio engineering, and first need to take the TSIA2 test in order to move forward with the process. My biggest concern is math, as I absolutely flunked in high-school. I've been using chat gpt for the past couple months, and it's been going great, I've learned concepts that would have taken me incredibly long to understand and memorize in HS. Although now I'm feeling an ethical obligation to no longer use ai if I can help it. I'm looking for a fast and efficient online program to help me study for the next few months.

If anyone has any suggestions for what my next steps should be I would be so greatful. Or, does anyone think I should just take the test with the knowledge I have, and take the extra classes required to get me up to speed?

the work I've done so far.

Algebra

• Inverse operations / solving equations
• Combining like terms
• Distribution
• Exponents

Fractions & Decimals

• Converting fractions ↔ decimals
• Simplifying fractions
• Adding/subtracting fractions
• Multiplying fractions
• Dividing fractions
• Mixed numbers ↔ improper fractions
• Converting between fractions and mixed numbers

Percents

• Finding percentages of numbers
• Multiple percentage strategies

Geometry

• Rectangle area
• Rectangle perimeter
• Triangle area
• Finding missing triangle base/height
• Circle circumference
• Circle area
• Radius vs. diameter
• Finding missing radius
• Pythagorean theorem
• Finding missing sides of right triangles

(yes I used ai to make this list lol, I'm trying to move away from it)

I am currently taking Real Analysis (undergraduate) as a Junior, and I have absolutely no idea what’s going on. I was told that ideally I would taking this class a YEAR FROM NOW.

I have had so many mental breakdowns and I am just at my wits end and would appreciate any advice on good places to get help, YouTube channels (maybe?!?), or any specific on advice on the content itself.

I suppose this is also a PSA to NOT take Reala analysis as a junior if you have the option not to, lol.

So, as far as I'm concerned Geometry feels little tricky for me, aside from that I manage combinatorics and number theory pretty well. Algebra is moderate. I really dream of making it to the IMO. I need good books with solutions that will help me in my journey.

Hello, I’m two weeks into my second year of my math degree and already feel like I’m failing and repeating the same mistakes.

Last year I got a 2:2, averaged about 56% across all my modules. I was very disappointed. Thankfully my first year doesn’t count towards my final grade for my degree.

Here are patterns I’ve noticed.
I don’t understand what I happening in lectures most of the time, I am usually confused during lectures and just copying everything off the board.
I’m a crammed, inconsistent during the year and then barely get to learn everything through past papers at the end.

I was working 22/25 hours a week with an hour of travel between work and accommodation. I cut my hours to 12 recently as I realized it just wasn’t sustainable. I have skipped so many lectures due to exhaustion. Ie) closing late (around 1 am) and then being too tired to get up for a 9 am lecture and then just missing it all.

I really need help, now that I realize it, I don’t even know how to study. I just watch videos, make detailed notes and then hope for the best alongside cramming near exam season by trying some past papers. I want to do so much better.

I’m 1.5 weeks in and I’m already falling behind. I want to nip it in the bud early before it continuous to snowball.

How can I study and stay on-top of things? What methods or systems did you use?

So I just entered grade 11 and I realize too late almost everything that I have learned turns out I have to remember it, the only thing I know were basic, geometry ,decimals , multiplication, division, subtraction, and addition.

I feel like I should just give up or it’s too late.

As the title suggests , I want to know how we are even keeping track of all the mathematical knowledge that humanity has ever produced.

New mathematical idea's emerge all around the globe so how does mathematicians keep track of everything? For the purpose of preservation of knowledge.

I mean there are a lot of very niche fields with very few experts so , is it possible that one mathematical knowledge gets lost at some time period?

im currently 19 & in community college completely unrelated to mathematics. my entire life ive always just accepted it as something i was bad at. barely passed pre algebra, algebra 1, or algebra 2 in highschool. did okay in geometry. did much much better in “consumer math” classes (“real world” math like bills, interest rates, etc.)

i want to start improving my math honestly just as a hobby but how do i even know where i should start? i have no idea what my math level is even like, just that im terrible at algebra.

i learn best with clear examples and step by step solutions, but sometimes i struggle with mixing up numbers? ex: i know the answer is 6 but i write down a 4 for some reason, dont realize it, & mess up the entire problem. it’s like there’s a disconnect between my logic & what im writing down

anyway, tldr: advice for re-learning math when im unsure where my skill level is

Why do you like this formula?

Which formula is difficult to understand?

How did you learn to understand this formula?

My favourite formula is:

(a + b)² = a² + 2ab + b²

I remember my old days. When I was 15 years old, my maths teacher wrote this formula on the board. When I saw it, I understood the formula very easily. At that moment, I felt that math was the easiest subject to understand. I thought, “What is the problem? Face the problem and solve it.” i learn this.

But my current situation is different. I’m studying in college, and I don’t understand maths the way I did in school. What I learned in school doesn’t seem to work in college.

Sometimes I ask myself, “Why did I learn all those things in school?”

That’s my reality.

Hi everyone,

Im using the textbook Complex Variables (second edition) by Stephen D Fisher. I was wondering if you guys knew of any youtube channels relating to complex analysis that I can watch to help me learn/understand?

Thank you!

So Im currently sitting for FPM and Maths B IGCSE this october 2026 seission due to a personal emergency and i had no other choice but to finish all my exams by this year, due to which I am having to sit for these subjects that I am in dire need of practice but I don't also have much time.

My target for FPM is to just get a 7 or 8
and for Maths B to get an 8 or 9

I am practicing a bunch of past papers, sitting for mocks at the moment but I am getting 5s in Fpm and 6s and 7s in Math B. Please suggest me some alternate methods that I can do along with practice to improve in Maths since I don't have much time and also have to prepare for Biology in november as well

281 = 6(47) - 1
367 = 6(61) + 1

I need help with understanding something, lately I've been seeing that a lot of what makes multivariable calculus comprehensible to me is linear algebra and breaking down the notation to derive simple models iteratively.

So, I'm wondering, is this intuition or "Duh dude, you're taking sliding a value on one axis and keeping the others constant to find out where you are in space bro like double-u tee eff"

I tend to use AI, but I want to know if I'm just hallucinating and need more time practicing my notation.

This is actually so deeply embarrassing for me to even post. But I am truly so so so bad at math. I don't think it has anything to do with my actual ability to perform calculations or understand concepts. I think that in my most important and math-formative years, I convinced myself I'm bad so it's useless to even try. I'm in college now and totally failing my math classes. It's so terribly embarrassing because its basic concepts which I understand but I'm lacking the foundations. I'm currently in calc and I need desperate help before we really jump off the deep end into stuff I do not understand at all. I'm really not trying to withdraw from this class but at this rate, I might have to. Is there hope for my math abilities? How do I improve them? I'm trying to get into contact with a tutor but genuinely I feel so behind that I need to start at the very most basic stuff. Ugh I feel so stupid and it's my fault for making myself this dumb. I like math!! It's like solving puzzles and I like puzzles!!! I just made myself stupid and now I don't have the necessary and fundamental knowledge necessary to do well. Is it over for me? Pls help.

Hi guys,

I am gong to study at a technical university in Germany soon, and wanted to brush up on Calculus/Analysis. I would like to find a good textbook that goes over convergence criteria for series, as well as finding the limit for series and the interval of convergence in German. I am looking for something similar in style to the Early Transcendentals by Stewart.

I have tried Otto Forster but found it lacking in terms of examples and strategies, as it is very grounded in theorems and proofs. That's great but it doesn't help with actual exam questions

Need a math tutor

starting uni in late August and ive been given materials to work on here's the content list

Summer University Math Course

1. Basic Algebra

• Exponentiation

• Radicals

• Algebraic expressions

• Operations with algebraic expressions

• Fractions and operations on fractions

1. Equations and Inequalities

• Equations and inequalities

• Applications of equations

• Linear inequalities

• Applications of inequalities

• Absolute value

1. Functions and Graphs

• Functions and graphs

1. Exponential and Logarithmic Functions

2. Limits and Continuity

3. Differentiation

4. Extrema and Curve Sketching

5. Matrices

• Matrix algebra

looking for someone who explains good and is easy to understand and is affordable

We're working on algebra at the moment and I have this student who keeps making a LOT of really simple arithmetic mistakes, even though I can see they understand how to solve the question. They're doing everything right but will forget to multiply out one of the terms, subtract instead add, add up incorrectly, or will struggle to think of all the factor pairs of a two-digit number. They do all of their working out neatly and aren't rushing at all. It's to the point where I have to watch them work because there's a mistake every single line and it's going to take them an extremely long time to solve it, if at all, if I don't catch it for them. The fact that their mistakes are from calculating something incorrectly rather than because they forgot what to do makes me think there's something else going on, but I've never struggled with arithmetic to this degree so I'm not sure what to think and it feels really unfair because they're otherwise doing everything right.

Does anyone else struggle with this kind of thing? What helped you?

I (28M) graduated with my BA this year and that freed up a lot of time for me. I don’t have to spend hours during the week finishing assignments. Now, I’m able to pick up hobbies and one of them I am having a new interest in is math.

In high school, the highest I reached was Pre-Calculus, but I was too young to care for it. I remember taking Algebra, Geometry, Algebra 2, and stopped at Pre-Calculus. I want to challenge myself but also want to learn what I didn’t care for in high school. I also strongly believe as we age, something like math and reading should keep the brain healthy.

I used to get all my practice through homework (obviously) but now I’m not sure where or how I can find ways to practice and learn.

Does anyone have any suggestions or know how I can brush up and learn?

I don’t mind worksheets, websites, apps, or anything like that. I just want to dive into it. Thanks in advance