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Forums - General Discussion - What math have you learned?

Nothing special, I had three semesters of calculus, two semesters of linear algebra, introduction to discrete mathematics/mathematical proofs, and some differential equations ...

Eventually I want to explore abstract algebra/algebraic structures, complex analysis, non-linear differential equations/dynamical systems/chaos theory, partial differential equations, and lastly real analysis ...



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Highest I went was Finite Mathematics. I don't wish to go any further though. My field really doesn't require strong math skills. Unless you want to program scripts for Maya or something which really isn't that hard.



Here are some awesome books for anyone interested in learning math or physics (in roughly this order).

 

Basic Mathematics (Lang) - This book covers the essential prequisite mathematics for calculus.  It's especially great for adult learners because it removes the fluff from most precalculus books (colorful pictures, cutesy word problems) and gets down to the nitty-gritty.  You'll even find a few basic proofs in here!

A First Course in Calculus / Calculus of Several Variables (Lang) - Lang was a great writer and a greater mathematician.  His introductory calculus books strike a great balance between rigor and practicality.  Calculus is one of the most integral subjects because it opens doors to higher mathematics, physics, chemistry, mechanical engineering, and many other disciplines.  

Physics (Halliday, Resnick, Krane) - Save some money and purchase the fourth edition.  Newer editions have cut out lots of interesting material, but added more colorful diagrams and links to interactive features on the internet.  You'll get a kick out of some of the dated problems about computer memory in the first chapter.  To the current physics students - ever wonder about the direction of the angular velocity vector?  You'll find the answer in one of the chapter appendices on axial and polar vectors!  :)

How to Prove It (Velleman) - If you want to continue to higher mathematics, understanding how to read and write proofs is essential.  In this book you'll learn how to construct proofs using the most common types and you'll pick up on a few basic theorems from number theory and abstract algebra.

A First Course in Probability (Ross) - Pick up an older edition to save money!  Probability comes up a lot in quantum mechanics and statistical mechanics, so it's important to get a good grasp on the basic concepts.  Remember the Monty Hall problem with the doors and the goats?  Read up to find the mathematical reasoning behind the counterintuitive solution!

 

Instead of bombarding everyone with tons of books, I'll keep it small for now and if anyone is interested in more books I'll write up another list tomorrow.  :)



Many. I majored in it.



e=mc^2

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I have take Algebra 1 and 2, Geometry, a semester of Math Studies, and am currently in Probability and Statistics. I really enjoyed Algebra 1 and Geometry and Im liking Prob and Stat right now, but I'm noticing that it really depends on the teacher who teaches me if I enjoy math or not. I found that for some reason math taught at a higher level refuses to explain the basics again in order to understand the more complex theories. Also They spend little to no time putting the math we are learning now into perspective with the other math we have already learned. Simple things like vocab terms help me tremendously in understanding the math we are learning yet they just don't teach it. It's as if they expect us to remember everything we have learned perfectly. Sorry Algebra 2 teacher, I don't remember everything from Algebra 1. Also instead of just teaching us how to do the problem, teach us the background of why we are doing these problems and to how these problems stemmed from other problems. It's really infuriating. My current teacher from Prob and Stat put it really well: "I'm always re-learning the material and vocab so I also do the same with you" She always gives us vocab and other things to really help us understand the material and its great. I could write a whole essay about this but ill just end it here.



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Superquagsire said:
I have take Algebra 1 and 2, Geometry, a semester of Math Studies, and am currently in Probability and Statistics. I really enjoyed Algebra 1 and Geometry and Im liking Prob and Stat right now, but I'm noticing that it really depends on the teacher who teaches me if I enjoy math or not. I found that for some reason math taught at a higher level refuses to explain the basics again in order to understand the more complex theories. Also They spend little to no time putting the math we are learning now into perspective with the other math we have already learned. Simple things like vocab terms help me tremendously in understanding the math we are learning yet they just don't teach it. It's as if they expect us to remember everything we have learned perfectly. Sorry Algebra 2 teacher, I don't remember everything from Algebra 1. Also instead of just teaching us how to do the problem, teach us the background of why we are doing these problems and to how these problems stemmed from other problems. It's really infuriating. My current teacher from Prob and Stat put it really well: "I'm always re-learning the material and vocab so I also do the same with you" She always gives us vocab and other things to really help us understand the material and its great. I could write a whole essay about this but ill just end it here.

The reason why we don't do a lot of review in post-secondary mathematics is ideally because it's simply more productive to cover new material ...

I've personally never felt the need to remember all the previous minute details for higher mathematics since losing some memories of the material covered in highschool algebra so I'm not sure if your over exaggerating. We are learning the background (sometimes) but you maybe in luck if your school has a course in history of mathematics ...



fatslob-:O said:
Superquagsire said:
I have take Algebra 1 and 2, Geometry, a semester of Math Studies, and am currently in Probability and Statistics. I really enjoyed Algebra 1 and Geometry and Im liking Prob and Stat right now, but I'm noticing that it really depends on the teacher who teaches me if I enjoy math or not. I found that for some reason math taught at a higher level refuses to explain the basics again in order to understand the more complex theories. Also They spend little to no time putting the math we are learning now into perspective with the other math we have already learned. Simple things like vocab terms help me tremendously in understanding the math we are learning yet they just don't teach it. It's as if they expect us to remember everything we have learned perfectly. Sorry Algebra 2 teacher, I don't remember everything from Algebra 1. Also instead of just teaching us how to do the problem, teach us the background of why we are doing these problems and to how these problems stemmed from other problems. It's really infuriating. My current teacher from Prob and Stat put it really well: "I'm always re-learning the material and vocab so I also do the same with you" She always gives us vocab and other things to really help us understand the material and its great. I could write a whole essay about this but ill just end it here.

The reason why we don't do a lot of review in post-secondary mathematics is ideally because it's simply more productive to cover new material ...

I've personally never felt the need to remember all the previous minute details for higher mathematics since losing some memories of the material covered in highschool algebra so I'm not sure if your over exaggerating. We are learning the background (sometimes) but you maybe in luck if your school has a course in history of mathematics ...

Yeah I guess I just have a harder tme remembering some of the material but I tend to learn better when I have an understanding of the bigger picture rather than the "what we have to accomplish right now". Also I'm just a slower paced learner in general and I struggle when I have so many different things to learn at once. Also I'm not saying we should spend a huge amount of time refreshing ourselves on every single little detail on the past material, but we should have SOME time to remind ourselves of the general world of mathamatics we are treading in. Also sorry if I seemed a little ranty lol. I'm just passionate in our education system and it frustrates me in how much some of our political leaders and teachers do not care about what we learn, and we end up suffering directly as a result of it.



some basic calculus is as far as I've bothered so far, we'll see in the future if I go further, not in love with mathematics



Superquagsire said:

Yeah I guess I just have a harder tme remembering some of the material but I tend to learn better when I have an understanding of the bigger picture rather than the "what we have to accomplish right now". Also I'm just a slower paced learner in general and I struggle when I have so many different things to learn at once. Also I'm not saying we should spend a huge amount of time refreshing ourselves on every single little detail on the past material, but we should have SOME time to remind ourselves of the general world of mathamatics we are treading in. Also sorry if I seemed a little ranty lol. I'm just passionate in our education system and it frustrates me in how much some of our political leaders and teachers do not care about what we learn, and we end up suffering directly as a result of it.

Well if you wanted to learn the "bigger picture" that pretty much requires you to major in mathematics ...  

Higher education is all about self motivation so I guess professors expect their students to handle reviews themselves plus there's always the option of community colleges where you can go at a slower pace too if one chooses to ... 



At university I took
- lineare Algebra 1 &2
- Analysis 1 &2
- Logik
- numerical Mathematics