I’m freaking out, I’m 23, haven’t done math since high school and starting a bachelors in October

I last did math when I was 18, since then I’ve been in the army, working and traveling. I remember super basic algebra,super basic geometry, and everything else is very hazy. There are lots of topics I never learnt like complex numbers, vectors, matrices, induction and probably more.

First semester includes calculus 1, algebra 1 and discrete mathematics.

I understand that I’m vastly under prepared for these subjects but the amount of things to learn is overwhelming and I only have 2 months. What should I focus on and in what order? Thanks!

submitted by Nevin Manimala Nevin Manimala /u/davegri
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Is there a concise way to describe inverse complex trigonometry functions?

I’ve been writing an implementation for complex numbers in Java for myself and have gotten stuck on hacking together the inverse trigonometric functions. I found these shortcuts helpful for implementing the direct complex trigonometric functions:

sin(a + bi) = sin(a) * cosh(bi) + cos(a) * sinh(bi)

cos(a + bi) = cos(a) * cosh(bi) - sin(a) * sinh(bi)

tan(a + bi) = sin(a + bi) / cos(a + bi)

But have struggled to find any such configurations anywhere online for asin, acos, and atan to create their complex implementations.

Are there similar formulas for the inverse trig functions? Or do I have to delve into writing them out explicitly?

submitted by Nevin Manimala Nevin Manimala /u/Smoates
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Why algebra, number theory and combinatorics are integrated into one single contests filed/subject?

Shing-Tung Yau College Student Mathematics Contests have been annually held for several years.
The website of the most recent contests by China: http://www.cms.zju.edu.cn/conference/YCMC/rules.html
The website of the most recent contests by Taiwan: https://sites.google.com/a/math.ntu.edu.tw/yau_csm/di-jiu-jie (Sorry, no English website provided by Taiwan.)
From the webpage of scientific and questions committee you can see that there are 5 contests fields/subjects: Analysis and Differential Equations; Geometry and Topology; Algebra, Number Theory and Combinatorics; Applied Math and Computational Math; Probability and Statistics.

Question: Could someone please explain to me: Why algebra, number theory and combinatorics are integrated into one single contests filed/subject? Do algebra, number theory and combinatorics frequently appear together in math (workings/researches) and thus are closely inter-related in math (workings/researches)? In what ways do they frequently appear together and how are they inter-related, are there examples that can help me understand?

submitted by Nevin Manimala Nevin Manimala /u/JIZHANHUANG
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Advice: Sustained passion vs burst of passion, interest, etc.

Hi all. I’m sure this sounds familiar to quite a few of you: I had a huge, long interest in high school but didn’t have much language to articulate it, other life factors limited the blossoming of ability. Then usually something happens to people, e.g. they start drinking a lot, they get depressed, they find other passions, etc, and eventually they find themselves without maths and worse off in some way, whether they are obviously miserable, or that they lack the fire in the eyes they once had.

What measures can one take to sustain fierce interest when faced with difficult work to progress? I’ve experienced passion wane over time before, and maybe it’s unrealistic to think mathematicians in industry and academia are in constant bliss, but every day recently, just like years earlier, I’ve been waking up excited to learn.

My passion has only just been reinvigorated and i’ve been picking up the material i’d neglected in undergrad so far, and this “emptiness” feels largely conquered. The analysis course i’m vastly unprepared for feels like it has awakened an inner drive, which has infected all parts of life but especially maths, including fields other than analysis.

However I can see that it will take a lot of work to reach interesting stuff, to be able to engage with the content, etc, and while it’s easy to read to about different fields/subjects in a single afternoon, the reality is that I’ve got 12 more weeks in this semester and it’ll be years before I’ll have tasted those spicy topics, e.g. functional analysis, godel’s theorems, random graph theory, etc.

I’m wondering if there’s any (good) advice which is more sophisticated than “be realistic and avoid depression”. e.g. “take a little while every day to remind yourself why you’re studying this, by recreational reading of motivating topics”.

submitted by Nevin Manimala Nevin Manimala /u/ThrowawayBrisvegas
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Why is a circle or a triangle not the simplest shape in projective geometry?

I am new to projective geometry and have been doing a bit of reading and came across a fano plane very quickly. But why is that the smallest shape? Wouldn’t a triangle be simpler? From what rules I have seen I haven’t been able to find out why a triangle doesnt work. It has a point for each set of lines and a set of points for each line.

submitted by Nevin Manimala Nevin Manimala /u/nicholashaynes1
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Is is possible to express all real numbers as a sum of powers of 2?

Is it possible to express every real number as a sum of finite length of 2k where every k is an integer? I know its possible to do for every possible integer, and I assume all integers. This is why computers work, but does this property hold for all reals aswell?

submitted by Nevin Manimala Nevin Manimala /u/tgtpg4fun
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