Mathematics Definition and 995 Threads

Hey guys , what is the best book to read about category theory ?

Hi, the title is self-explanatory. I am wondering if there is something I can do to be able to read mathematics like I am reading a newspaper or book. Regardless of what the single letters are describing in natural language, I can understand -but maybe not conceptually grasp- what is being...

To give you a sense of strong induction and the relationship between mathematical induction and recursion (next session), let's do the pile splitting problem: Take a bunch of beads, rocks, coins, or any kind of chips. Ten is a good number. Split the pile into 2 smaller piles and multiply their...

Hello, I am currently pursuing my degree in Mechanical Engineering, and was wondering what math courses were good to take after the basic math sequence has been completed (Calculus 1-3, Differential Eq & Linear Algebra.). I have an interest in mathematical modeling and data analysis, as...

For a mathematical methods course, the end of year assignment is to study and present a topic in mathematics of my choice. I'd like to pick something directly related to electrodynamics that will prove to be useful later. However, I have very little idea of what is used in electrodynamics! Does...

Hello, I am new to posting on this forum so I will give some background. I am 15 as of tomorrow and I am a mathematics enthusiast. I also consider myself a proficient java developer. Some other general bits of info are that I have an interest in physics and astronomy and I was also, two weeks...

This is not about counting change for point-of-sale transactions; how does retail use Mathematics beyond intermediate algebra? Or does retail business use much or any Mathematics beyond intermediate algebra? Anything like with linear algebra, or linear optimization, or any sort of topics to...

I'm doing Bachelor Degree in Mathematics and have difficulties in study because every time I study I tend to ask "what" and "why" instead of "how". As a result, I often trap myself into the metaphysics and philosophical part of mathematics and unable to proceed further. I tried to ignore it but...

Well, I didn't know where to post this rather philosophical stuff, so decided to put it here. But I promise it is related to all sciences mentioned above. Here is the setting. Whenever we prove something mathematically, we always think that the proof is "eternal", often contrasted with the...

''This Invitation to Mathematics consists of 14 contributions, many from the world's leading mathematicians, which introduce the readers to exciting aspects of current mathematical research. The contributions are as varied as the personalities of active mathematicians, but together they show...

any suggestions for books/authors which contain these topics. Fundamental Concepts Of Mathematics Algebra of sets and logic; methods of proof; functions and relations; logical nature and structure of mathematics; introduction to number-theory; algebra arid geometry of complex numbers

I am feeling quite low. Let me start by telling you a bit about myself. As a child I was always asking "why?" I was also very curious. When I got older I found I was not bad at "math" and science. I read books like men of mathematics and biographies on Feynman and I began to form plans about...

Hi guys, I'm quite surprised that I'm interested in this. I've never really thought how wide and interesting Mathematics can be outside of normal plug-and-chug, computational or arithmetic based Math. Yes it can be challenging as Spivak's Calculus book shows it, but I find myself being glued...

Hello, I am in a bit of a dilemma. I am right before my undergrad degree and I have been torn apart between physics and mathematics. I have never really studied physics, very little in high school, but it seems fascinating to me and I figured that just because I didn't have a chance to study...

Has anyone read..."Mathematics and the physical world '' by Morris kline? what are your views on it? not sure whether I should read it, or go to a specialized book,but I want to learn some basic physics or math from it.

I have hard somewhere the story of mathematics professor(It maybe fake:biggrin:). The math professor was very strong in his concepts and had very good ability to solve math problems. Due to popularity among his peers and other mathematicians, his name spread throughout the entire city where he...

Hello, I'm a European EE/Engineering physics undergraduate (something of a mix of those two) trying to figure out what to major in. Up until now my main topic of interest has been nanotechnology. Now I'm not sure that's a good idea because of the seemingly small job market where I live. I want...

Use a truth table to determine that "division into cases" rule of inference is valid.

How many comparisons are performed to find 13 in the following list by using Binary Search? 7, 12, 5, 22, 13, 32 Is it true that there are 10 comparisons performed to find 13 in the following list by using Binary Search? If this isn't right, then can somebody please help explain this to me?

How many vcomparisons did you actually need?

If you could describe mathematics / physics in one sentence that covers Archemedes through to Einstein, what would you say? Your answer can be mathematical or even just a single equation. The as a separate question: If you could bring back 1 mathematician / physicist from history, who would...

Hi all! I'm a mid-20s guy from Montreal , Quebec , Canada completing his high school mathematic courses at an high school for adults with the eventual goal of entering a bachelor program in mathematics (probably either at McGill or Universite de Montreal (UdeM)). Basically I'm worried about...

Hello guys: A very known fact we live is that mathematics is not falsifiable. There hasn't been a day in history when someone came up and made an experiment to prove that the equation "x^2-5x+6=0" has solutions different than 2 and 3. In science, if we find something that doesn't comply...

I need some advice, I've just finished my 2nd year at UCL studying the Bsc in mathematics. I've so far really enjoyed my course and I'm hoping to go on to do a phd somewhere. Now, like everyone else, I want to go to the best place possible. So far, my grades are fairly good, every exam...

Since there are tons of people here who're good reviewers what 's you take on this little book ?is it good to use it for physics ?or does not explain things deeply enough?look up the amazon page https://www.amazon.com/dp/0486660974/?tag=pfamazon01-20

A book that goes very much in depth, explaining and reasoning out every topic is the book that I prefer. The topics I require are: Unit-I: First order Differential Equations (10) Formation – Variables seperable – Homogeneous, non Homogeneous, Linear and Bernoulli equations. Exact...

Hi Everybody, I am in my final year of high school, and want to enrol with the University of the Witwatersrand in Johannesburg, South Africa next year, and I will hopefully be going for a Bsc in computer science, math and physics. However, I have been wondering a couple of things over the...

Hi all, I'm currently double majoring in applied mathematics and physics and minoring in computer science. I'm about 2 years away from graduating and I am starting to freak out because I don't know what I can do with my majors and minor. I don't know what kind of internships I can do with my...

I know that this was done in the late 1500s and early 1600s and even al khwarizmi الخوارمي in the 9th century did a lot to formalize math. I'm pretty sure fibonacci (not his real name) did not write his famous book using notation. I know Descartes did a lot to formalize math but the other...

I am having a hard time solving word problem like those that you have model an function to find the right answer. This would become very problematic in the next semester since I will take Calculus. I have taken pre-calculus,but the class didn't require me to solve modeling problems...

I apologize if there's any mistake in my question or argument as I don't have an advanced education in mathematics (haven't seen anything beyond first year calculus with the exception of partial derivatives in a purely thermodynamic context) so please do correct me if I'm wrong. I can't...

Math is able to prove and disprove things while science can only disprove. The reason we can't prove much about the actual world is because unlike in mathematics we don't have enough starting axioms. If the math world isn't real and is just an object of the mind it would make sense that us...

Hello all, I am new to this forum thing when it comes to mathematics and science but I have found much help on other issues thanks to this wonderful thing we call forums online nowadays. Anyway, my dilemma involves trying to make a change (course correction) in my current path to a career. I...

Will it be hard to take calculus I at Night during three hours from 6 to 8:45?

i found this problem interesting in stack exchange unfortunately i will participate in discussion for 4 days(vacation) inequality - Prove $\sum_{i=1}^{n}\frac{a_{i}}{a_{i+1}}\ge\sum_{i=1}^{n}\frac{1-a_{i+1}}{1-a_{i}}$ if $a_{i}>0$ and $a_{1}+a_{2}+\cdots+a_{n}=1$ - Mathematics Stack Exchange...

What would you recommend as the best book for engineering in mathematics? Something with a great insight and depth, and very well explained. With good exercises too. Here's the chapter it's required to have: Partial Differentiation: Introduction to Partial differentiation, Total...

Hey guys- I know many of you may not be in medical school- but I'm interested in rekindling my math knowledge- mainly to expand my options as a future researcher. I just finished my second year- and this upcoming year, based on rudimentary calculations I should have 4-5 hours of time after...

Do I Need Calculus or Another Advanced Mathematics to Use This Book? I would like to learn the material from the first to the sixth chapter in An Introduction to Mathematical Thinking: Algebra and Number Systems. Here are the topics in the book...

Hi, everyone! Well, I'm currently a math major at university, planning on going BS -> MS -> PhD, and then being a professor. The problem is, I'm not sure if this is a good career path. Can anyone give me some insight or advice into this? Thanks.

Hello, I read that many people believe mathematics to be simply an extension of logic and therefore some or all of math to be reducible to logic. I thought this was an obvious fact for the longest time. I was wondering if there was any flaw with such an argument or what else there is which...

I'm in my last year of school and starting a mathematics degree at a British university this Autumn. I've always liked mathematics, especially 'pure' side of mathematics. I love poofs and always enjoyed solving puzzles and brainteasers for fun. Some of my favourite topics of maths are geometry...

As an aspiring theretical physiciat, besides the general concept and its applications, as well as proficiency at dealing with a certain mathematical ''thing'' (identities, properties, theorems, techniques...) should I focus too on the demonstrations, proofs or I just have to take them from...

I'm a student of a university in Japan. I'm enrolled in correspondance course. I'm a philosophy of science major. I need to study mathematics and physics basically.I think I need to study maths and physics or other subjects in English. I can barely understand them in Japanese because Japanese...

Hello I would like to know if there are any good textbooks that can teach mathematics in relationship to physics or explain the usage of popular physical formulæ. I am a hobbyist and I need to have a better understanding of the Calculus problems that I am dealing with while I am working on...

are there are disproportionate number left handed people in math and physics? there are a huge disproportion of lefties in architecture, because their right brain is better developed. they can better visualize in 3-d. anyone got more info on this?

I'm trying to go through Shannon's paper "A Mathematical Theory of Communication" to improve my understanding of information theory. In Part I (Discrete Noiseless Systems) Shannon states: Suppose all sequences of the symbols S1, . . . ,Sn are allowed and these symbols have durations t1, ...

So far after observing the math I've been learning for the past 10 years of my school career it seems to me like everything can be simplified into addition. Ill show by example; Addition: obviously Subtraction: Addition of negative numbers Multiplication: Repeated Addition Division...

The formula for producer surplus is: Income - expenses = P*Q - ∫M(Q)dQ However, shouldn't it be P*Q - (∫M(Q)dQ + FC), with FC= fixed costs? I mean, the marginal costs are just the derivative of total costs, and thus integrating them is the same as just integrating the variable costs, ignoring...

Hi, I was just working on a problem based on the probability of wind or rain. The only way to solve it is to assume they are dependent factors when they clearly are not. Assuming independence will lead to the wrong conclusion. If stats demands one ignore reality to solve a problem, to bend...

Hi guys, I'm an undergraduate in a mathematics & economics double major right now. I have struggled pretty hard with math in the past (even failed many times) but I have pretty much developed the resolve to see it through because I enjoy it and I think the challenge is actually quite...