What is Mathematics: Definition and 997 Discussions
Mathematics (from Greek: μάθημα, máthēma, 'knowledge, study, learning') includes the study of such topics as quantity (number theory), structure (algebra), space (geometry), and change (analysis). It has no generally accepted definition.Mathematicians seek and use patterns to formulate new conjectures; they resolve the truth or falsity of such by mathematical proof. When mathematical structures are good models of real phenomena, mathematical reasoning can be used to provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry.
Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.Mathematics is essential in many fields, including natural science, engineering, medicine, finance, and the social sciences. Applied mathematics has led to entirely new mathematical disciplines, such as statistics and game theory. Mathematicians engage in pure mathematics (mathematics for its own sake) without having any application in mind, but practical applications for what began as pure mathematics are often discovered later.
I have finished my undergrad in physics and am thinking about going into a postgrad in mathematics. Since I did not major in mathematics how hard is this going to be?Is it going to be very different?I have done a lot of reading on my own and I think I may be able to cope and catch up anything I...
Hello,
I am seeking the opinion of mathematicians. I want a solid understanding of pure mathematics. I would like your opinions on where to start.
My background in formal mathematics courses ended with the standard calculus series. I pursued no further classes while attending college...
When reading about Gödel's incompleteness theorem(s) a few years back, I vaguely remember reading the statement that one of their implications was that mathematics can not really be seen as "merely" logic. I think the reasoning was something like: since we have sentences "this cannot be proven...
Before I begin, I apologize for any bad English, it isn't my first language.
I'm a medical student who didn't do any mathematics for 3 years. However, after finding out the "plug 'n chug" approach isn't really what mathematics is about, I became interested in learning it from the basics all...
The history of mathematics...help with resources
Hey guys I need help finding good resources to help me understand basic to advance math from a developmental point of view, the applied necessities of the inventors of math operations and concepts.
For example the addition operation was...
The title is essentially dual to the one in blogposts of Nielson and Gowers, from which Polymath wiki developed. The subject is the same here, although different in the sense that whether or not that is possible in forums.
A member of this forum have tried to start a polymath project here on...
i'm a mechanical engineer student, 1st year.
currently follwing erwin kreyzig, I am intersted in solving complex type of problems but couldn't find much in erwn kreyzig. it has only beginninng level easy questions.
is there a book that you can suggest which has tough and complex...
Hi everyone, just something for us to discuss. I have always been taught to use a full stop for a decimal point, and a centred dot to represent multiplication. This appears consistent with the output of CAS calculators and software. However, it appears that it people in older generations (I'm...
Hello,
I'm new to this forum so please bear with me! I am a Math and Mechanical Engineering Double major who is considering getting my PhD in Math. I want to become a Math professor after I receive my PhD, and I have always had a love of airplanes, so I was wondering if there are any topics I...
First off a little about myself as I'm rather new to the forums. I'm currently pursing a degree in management of engineering sciences at Embry-Riddle Aeronautical Univiersity. I really enjoy mathematics, not just soliving equations but reading about the history of it and the great thinkers of...
After harboring the aspiration to read Astrophysics and Mathematics (I love all things adhering to abstract and logical reasoning; as such game theory, logic, military strategics, mathematical proofs ), I'm now in a 4 years double major undergraduate program in one of the well-know prestigious...
Good evening guys,
I now announce that I am entering the second *hard* half of mathematics, in college!
Courses I have finished:
Calculus I
Calculus II
Calculus III
Differential Equations
Linear Algebra
Foundations of Mathematics
Operations Research
I am registered for two math...
First of all i must admit that i am not sure if it fits into academic guidance or career guidance category.
I am senior student of physics in my country's one the best universities. This was the bright side. I am 26-27 years old, i am about to graduate in 1.5 years. I was always considered as...
I was looking for a self-study book that is accessible by an high-school student (11th grade) for general relativity. I read reviews on "A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity" but unfortunately, it isn't available here, in India...
Hello,
I'm in need of some advice.. I'm currently majoring in physics, but I've been thinking about changing my major. I'm in physics 1, and struggling because I have a bad professor who can't seem to teach the class.. I originally wanted to go to grad school to continue my studies as an...
Hello, I am from Ontario, Canada. I will be graduating from high school soon, and right now, I have to take care of my university application.
First of all, I am interested in pure mathematics because I really like rigor, proofs etc. Thus, my choices so far are the mathematics programs from...
So, recently i found out that Ramajuan's math is highly applicable and usable in modern physics(things like string theory and stuff) so i decided to start learning more about his work and i stumbled on some questions.
1.What kind of math background do i need before diving into Ramajuan's work...
I've taken differential,integral,multivariate calculus, DEQs, Introductory Linear Algebra, and am currently taking complex analysis and vector calculus (an extension of vector calc from multivariate). As a math student, how do you decide what to study after that? Is it time to specialize?
I...
I'm from the UK and began my bachelors in mathematics around a month ago, with the hopes of going on to further study afterwards. My university is one of the best for mathematics and so far I've aced all my previous exams so this is quite a big shock to me.
I'm struggling with near enough...
I have encountered this problem in its general form: finding a^k mod n, where k is a rather large number. I have been researching on the internet for several hours but I still don't understand it well. Can anyone provide a detailed explanation as to how to solve this kind of problems?
I'm trying to understand the math behind Hooke's law and work done by a spring. I'm really looking for clarity. I am trying to understand why after integrating the equation I get three different results. I understand that each formula is specific to a problem but why does this work...
I realize it's a very broad statement to say that I'm independently learning mathematics because I am definitely not learning all of mathematics. I am currently studying the calculus and of right now via M. Spivak and have also been consulting R. Courant's Differential and Integral Calculus, vol...
How would one go about attaining a dual doctorate in math and physics? Would I be able to do both at the same time? Do people usually go for the doctorate after bachelors?
What colleges allow such a program?
thanks.
Homework Statement
Twice the supplement of angle 0 is 104 degrees greater than four times the complement of angle 0. Find 0.
Homework Equations
The Attempt at a Solution
I'm not sure where to begin. I'm good with angle relationships, all I need is the equation.
Hi all, I'm a student in Mathematical Science in which I'm specialising in Mathematics and a little Computer Programming. I love Maths and definitely have a flair for it. I'm also extremely ambitious and am massively motivated by money, I love it. :P Ideally I'd be earning over 250k or even more...
Homework Statement
Has anyone here read The Mathematics of Juggling by Burkard Polster? I am having a hard time understanding how the inverse of a juggling sequence is calculated on page 27.
For example, the table on the page has 7 rows, and in the fourth row, I'm not sure if that symbol...
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...
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?
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...