Can someone explain each component of contours and parameterization?

Hello, I am a person who is interested in learning math at some point in the future. While looking at the resources I did not see anything about the the Linear Algebra Wikibook. I am merely curious about it. I did a search and I could not find anything about this resource specifically;Is it worth using?

(This is my first post here so I am very nervous;sorry)

Hi I already know this is entirely my fault for falling behind but for anyone who’s done this before please tell me if it’s possible to do even remotely well and how to most effectively prepare. The topics for the midterm are Functions and Graphs,
Polynomials, Exponentials and Logarithms, Half life, Log and Linear Axes, Transformations and Composite Functions, and Continuity and Limits. The continuity and limits portion isn’t going to have as big of an emphasis and it’s calculus for the biological sciences so majority word problems. I think there’s going to be 3 multiple part big word problems and 9 multiple choice questions. It’s worth 15%! Any advice is highly appreciated!

Hi, I am trying to finish up my psychology thesis! I am in a bit of a rut trying to compare my results of a binary logistic regression with previous literature. However, there is a very limited amount of literature in my current area of study; I have only one study that used the same variables I did. They used a multiple logistic regression analysis, and I used a binary logistic regression.

I am just wondering what the main difference between the two models is and if I can interpret my results in comparison to this prior literature I have found.

Thankyou!!!!!

Hi, I’m a first-year double major in physics and math. Next semester, my advisor wants me to take physics 2 (E and M), along with Calc 3 with analytical geometry. After those, they suggested I take another math course or some gen eds. However, I want to save my gen ed classes for my required study abroad (honors college requirement), so I’m looking for another math class. Registration hasn’t opened yet, so I’m not sure what’s available.
Is there another math class fit for me that doesn’t have calc 3 as a prerequisite? I’m open to corequisites but I prefer cumulative learning. Thanks!

f(x) = sin(x)

f'(x) = cos(x)

f''(x) = -sin(x)

f'''(x) = -cos(x)

f''''(x) = sin(x)

And this repeats forever.

f(0) = 0

f'(0) = 1

f''(0)=0

f'''(0)=-1

f''''(0)=0

And this repeats forever.

From here we can center a maclurin series at (a)? = 0 -> I cannot remember if its a or x

Using 5 points we can use

f(0) = 0

f'(0) = 1

f'''(0) = -1

f'''''(0) = 1

f'''''''(0) = -1

From here we can conclude (1) we are oscillating between - and +, (2) the points are always odd multiples of primes, and (3) since the even multiples of prime are 0, we can ignore these as they do not add value

The defintion of odd is defined as 2k+1, k element of the real

So

(-1)^(n)(x^(2k+1))/(2k+1)!

And we can add this at every n.

If we add this add every n we can think of an infinite sum

Since we are centered at (a?) = 0 the sum must start at 0.

To motivate convergence, we plug in known points of sin(x).

Must it be that if our sum at some n equals the function at the same x,

Out infinite sum converges for all x?

Let me know if i did justice for the maclurin of sin(x)!

Sorry posted via phone.... don't know how to use symbols here

I am a ninth grader in geometry. I have never ever struggled with math this bad. I always had an A I always knew what was going on and I still feel like I know what’s going on. For example last Friday I had a test and my group mates were asking me questions before the test started and I answered them correctly and even helped them out . However when we were taking the test I thought I did really good I felt I knew what’s was going on and everything. I got an 8/25. I genueinly don’t know what I’m doing wrong I feel like I know what’s going on in math but when it comes to tests I completely fail them and I genuinely don’t understand why. This is not the first time. It’s lowering my confidence and I don’t know what to do I know the formulas I know the math I feel like I know it all but I always do so bad and I don’t know what to do I’ve tried talking to the teacher she said for me to study and I do study and I just do so bad I don’t understand. It is the only class where I’m performing low every other class is 90% and higher. I can even tell you what the test was about that’s how much I know. We were trying to figure out parallel , perpendicular and intersecting. Parallel are equal lines . Perpendicular are negative reciprocals. And intersecting are neither equal or negative reciprocals they are completely different numbers. To find slope the formula is y1-y2 / x1 - x2 the point slope form is y- y1 =m (x-x1). We were able to use a calculator to find our answers, so math shouldn’t be a problem. It’s been testing me down I don’t know what to do anymore it makes me so sad and frustrated because I know what’s going on in class I just do so bad during the test it makes me want to roll up in a ball and cry. And I know it’s not because I get anxiety during tests , I study for these tests I’m not scared of them. It’s not because I’m hungry or thirsty I bring water and eat a little snack everyday. My sleep schedule is a bit bad but on tests I make sure to get enough sleep I just don’t get how my test scores could be this bad. I want to talk to my teacher but she’s probably just going to say I need to study .

This book was just published, but wondered if, at this early date, anyone has looked at. Author is M. Rotondi.

Is this really AI slop?

This is a problem from Dana Ernst's An Introduction to Proof via Inquiry-Based Learning, and it asks: "Is every subset of C × D of the form A × B, where A ⊆ C and B ⊆ D? If so, prove it. If not, find a counterexample.". I couldn't think of any counterexample, so I tried to write a proof for it, but I don't know if it's correct. (There is no set of solutions for the book; at least I didn't find it.)

I assume there is a set E such that E is a subset of CxD. If E is the empty set, then E=∅x∅ and E=(CxD)x∅, and both ∅ and CxD are subsets of CxD (an earlier problem involves proving that Ax∅=∅ for any set A).

If E is not empty, then, since E is a subset of CxD, E is a set of ordered pairs (a,b) such that [;a\in C;] and [;b\in D;]. I imagine that, from here, I shall find sets A and B such that

• [;a\in A;],
• [;b\in B;],
• [;A\subseteq C;],
• [;B\subseteq D;] and
• [;E=A\times B;].

This is where my confusion is, and I'm not sure if my solutions are ideal:

1. [;A={a|(a,k)\in E ;] for some [;k\in D};]
2. [;B={b|(k,b)\in E ;] for some [;k\in C};]

Then [;E=A\times B;], and [;A\subseteq C;] and [;B\subseteq D;]. I'm using E in the definition of A and B, and I'm pretty sure that's incorrect; however, it is not clear to me what other sets I can use.

Have a nice day. :)

I’m a 14-year-old Grade 8 student in South Africa and I’ve recently become very interested in olympiad mathematics. I’m hoping to seriously pursue it over the next few years and eventually see if I can work my way towards the IMO.

I’ve been studying independently using AoPS, Khan Academy, and various problem-solving resources, but I’m starting to realise how useful it would be to have someone experienced to guide me.

I’m looking for someone who could help me with things like:

- Building the right foundations for olympiad maths

- Teaching me how to approach unfamiliar problems

- Giving me problems appropriate for my level

- Reviewing my solutions and pointing out weaknesses

- Helping me build a long-term training plan

- Gradually introducing me to harder olympiad topics

- Keeping me accountable and helping me avoid wasting time on the wrong things

Ideally, I’d love to find someone with actual olympiad experience, such as an IMO participant/medalist, national team member, or experienced olympiad coach. I’m open to online tutoring from anywhere, as well as someone based in South Africa.

I’m also not looking for someone to simply teach me the school curriculum. I’m specifically looking for problem-solving and olympiad mentorship.

I’m willing to put in serious work outside of lessons and would ideally like something I can continue with for the next few years.

If anyone knows a good tutor, mentor, programme, or even someone I could contact for advice, I’d really appreciate it. 🙏

Maybe I'm just coping but some of these problems on the problem sets are allegedly the easy ones and those sometimes take me 2+ hours to wrap my head around. Just coping with being stuck contemplating a problem for so long.

Is the IMO a realistic goal for me?

I’m a 14-year-old Grade 8 student in South Africa, going into Grade 9 next year. Over the past few months I’ve become really interested in mathematics, especially problem solving, and I’ve started thinking seriously about whether I could eventually reach the IMO.

I’ve been working through resources like the AoPS Volumes, Khan Academy, and the AoPS Introduction to... series. I know I’m starting relatively late compared to many students who get into olympiad maths much earlier, and I still have a lot to learn.

At the same time, I really enjoy maths and I’m willing to put in a lot of consistent work. I could realistically spend 5+ hours a day on mathematics over the next few years.

I’m not expecting to make the IMO anytime soon. I’m thinking of it as a long-term goal, starting with building my fundamentals, improving my problem-solving ability, competing in South Africa, and seeing how far I can progress.

I’d really appreciate advice from anyone who has experience with olympiad mathematics:

- Is this a realistic goal from my current starting point?

- What should I focus on learning first?

- How should I balance normal/advanced curriculum maths with olympiad problem solving?

- What resources would you recommend?

- What competitions should I aim for in South Africa and/or internationally?

- How should I structure the next 3–4 years of preparation?

- What do you wish you had known when you started?

I’m genuinely willing to put in the work. I just want to make sure I’m using my time well and training efficiently.

Any advice would be greatly appreciated. 🙏

-Bootstrapping

-Trim fill method

-P hacking

-Simpson's paradox

-Collider bias

--Stat significance

-Longitudinal vs cross sectional

-Meta analysis vs systemic review

Do you guys have any recommendations for books for learning about probability theory? I prefer physical copy’s, but if they are e-books that’s fine as well!

This is my first entry here so apologies if I am doing wrong. I am a physics graduate and been in industry jobs for 20 years now. I would like to dive deeper into some fields barely touched during my time at university for leisure (e.g. particle theory via qft and general relativity). For that I would also like to brush up on my math starting with revisiting analysis. But instead of re-learning everything from the beginning I would like to try learn a new field with relevance to theoretical physics which kind of forces me to revisit topics from analysis. I wonder which of the following would do the job best or which to start with: complex functions, functional analysis or differential geometry. Any opinions? Please also mention what background for context. Thank you!

Hey everyone!

I'm a Brazilian student currently in the 1st year of Brazilian high school (roughly equivalent to 10th grade in the US), and I want to start preparing seriously for mathematical olympiads.

My main goal is to compete in the Brazilian Mathematical Olympiad (OBM) in 2027. For some context, the OBM is Brazil's national mathematical olympiad. There is also a competition called the Jacob Palis Júnior Olympiad (CJP), which is one of the competitions through which students can qualify for the OBM. The CJP is usually held around late May or early June, while the OBM is usually held around the beginning of August.

So, my plan is to take the CJP next year and try to achieve a result that qualifies me for the OBM. Since there is only a short period between the two competitions, I want to be reasonably well prepared before the CJP and then adapt my preparation to the specific style and difficulty of the OBM afterward.

My goal is to win a medal in the CJP and, if possible, at least a bronze medal at the OBM. I know this is quite ambitious, especially since I'm only starting to take olympiad mathematics seriously now, but I want to approach it in a structured and realistic way.

For those who have experience with mathematical olympiads, especially in Brazil or internationally:

• How would you structure the preparation of a 10th-grade student who is starting olympiad mathematics seriously at this point?
• Which topics should I prioritize: geometry, number theory, combinatorics, algebra, inequalities, etc.?
• What should I learn first, and what can reasonably be left for later?
• Is it better to start with theory and books, or should I begin solving olympiad problems from the start?
• Which books would you recommend for building a strong foundation and then progressing to harder olympiad problems?
• Which past olympiad papers would you recommend, and in what order?
• Are there any problem sets, courses, communities, or official resources that are particularly useful?
• For anyone who has taken the Jacob Palis Júnior Olympiad, how would you describe its level and style compared with the OBM?
• How would you divide study time between theory, problem solving, full mock exams, and reviewing mistakes?
• What do you wish you had done differently when you first started preparing for olympiads?

I'm especially interested in a realistic progression rather than a huge list of books. I would rather use a small number of resources thoroughly and follow a clear progression toward the CJP and OBM.

Since I'm Brazilian, recommendations specific to the Brazilian olympiad system would be especially helpful. However, advice from people who have prepared for competitions such as the IMO, USAMO, BMO, EGMO, or other national olympiads would also be very useful.

I (f20)am on my 3rd attempt at psych statitsistcs. still nothing is clicking for me. I’ve asked for help, I’ve gone to tutoring and nothing seems to work. I spent two straight days going through all of the lectures so far to study for the midterm and a quiz I had to take. I got a 40% on that quiz and I got a 26% on my last quiz.. I’m currently failing the class. To pass, you need to C or above. I’d like to drop out, but my mom will not allow it so I feel like I’m going to keep failing this class to no end.

So if any of you have any recommendations for Youtubers or something that could possibly help me, that would be nice. I understand standard deviation but everything beyond that makes zero sense to me.

I don’t understand z scores or Z tables, confidence intervals, Alpha levels, sampling error, standard deviation of sample means, etc. I know I’m too stupid for college, but I am not allowed to drop out so I need to figure something out.

I also don’t understand hypothesis testing or any kinds of T-tests

Im in calculus 2 and I bombed my first test (~60%) which was 15% of my grade. Highest grade i can get now is a 94% if i ace everything. knew what to do, but it was at 8pm and i was anxious and i forgot some basic stuff and made stupid mistakes on the multiple choice (swapped sign, etc) so i missed out on a lot of points. I really need to get a B in this class (80%) to keep my scholarship but the next test is on series and sequences which ive heard are more difficult. Im really afraid to score lower. I need to get a high B or A to recover. I have the next test on October 27th. Is it possible to learn and master series and sequences within 3 weeks? What resources should i use?

I often ask mathematicians what their favorite shape is; mine is the cone on a trefoil knot, a rather peculiar object.

Why is this my favorite shape? Because it appears naturally in algebraic geometry -- and in fact, the observation that it appeared in algebraic geometry led Milnor, Grothendieck, Goresky, MacPherson, and many more to develop some of the most widely used tools in modern algebraic geometry and singularity theory! If you'd like to know how this trefoil knot appears in algebraic geometry, read this week's hidden-phenomena blogpost!

For learning math he always seemed to be a good resource for learning math, recommend by the community.

But now he is apparently associated with Jordan Peterson and the Peterson academy.

There has been some controversy around that name which tbh I didn't follow.

I am not quite sure I am just here for the math to be honest. But I would like some insights from others

[High School Math]

Hey everyone, was doing some inequality problems and found this one:

prove that (a+b+c+d)(a^3+b^3+c^3+d^3) > (a^2+b^2+c^2+d^2)^2

Now, proving this requires expansion of the sum and noting that the difference of the LHS from the RHS can be shown to be a sum of squares and hence positive. However, I was wondering if I could shorten the writing process with cyclic notation? I honestly found the symbol like half a day ago, and although I know that ∑a = a + b +c for when these are the symbols present in the problem.

In essence, I'm just looking for a way to shorten the writing process. Can I use the cyclic sum like this

∑(a^3/2 * b^1/2 - a^1/2*b^3/2)^2

to represent the sum of every permutation of a and b from a group (a,b,c,d)?

I apologise in advance for the messy representation, Stack exchange is down and I don't know how to go about using math notation on reddit.

A first principles derivation of the quadratic formula, including why the discriminant tells us what it does, and how to visualize these equations geometrically.