What is Mathematics: Definition and 996 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.
Last year I got volume 1-3 of the Feynman lectures but as a soon mathematics major I think it'd be appropriate to read more mathematics lectures (and more enjoyable). Is there anything similar I could ask for for my upcoming birthday?
Thanks,
When did you first encounter "proof based" mathematics?
I've been reading a few forums and have seen many posters say "methods based" mathematics like calculus is easy. The posters would then state that "proof based" mathematics is so hard and calculus isn't high level.
So when did you...
Hello,
I am currently a Chemistry major, and I am really good with sciences.
My problem is with math ( Calculus), in fact I always had trouble with mathematics. The problem with my situation, is that I am really interested in Math Application, in addition I really need it for my major. So I...
Hi!
I have an argument and I have to prove the validity of all possible ways.
I have proved by logical implication, tautology, contradiction and contrapositive, but the problem is reduced to prove the hypothesis by logical equivalences and implications.
The reasoning is as follows...
Hello!
I am living in Germany. Let's say that I want to know the local time in New York, and let's arrange that the local time in Germany is 11:00 o'clock (24-hour clock).
Germany's time is shifted 1 hour ahead (UTC +1), and New York's time is shifted 5 hours behind (UTC -5). So the...
Homework Statement
James bought a house worth $308,000.00 and financed 85% of that amount. He has a 30-year loan at 4.82%. How much will he owe on the house after 12 years?
Then find the equity that James has from Item #4 above. His equity is the difference between the new value of the...
Why does mathematics deal with the world of perfect spheres, triangles and squares. I understand how this can be applied to architecture and engineering. But this seems counter-intuitive to 'nature' that surrounds us which is objects that are not perfect in shape. The Earth for instance isn't a...
Displaying Mathematics in Google Drive??
Hey, How can I display math written in word with google drives (cloud storge)? I'm trying to create a google drive for my class at university, but we can't view mathematical equations written in word documents with google drive.
Would appreciate some...
Homework Statement
Determine which row of pascals triangle contains 3 consecutive entries that are in the ratio 1:2:3.
Homework Equations
(n, k ) = n!/k!(n-k)!
The Attempt at a Solution
(n,k):(n,k+1):(n,k+2)
1 : 2: : 3
What I did was cross multiply.
2 times (n,k) =...
Hey
I am looking for a book talking about history of mathematics
Steven Krantz has one here
Amazon
Amazon.com: Customer Reviews: An Episodic History of Mathematics: Mathematical Culture through Problem Solving (Maa Textbook) (Mathematical Association of America Textbooks)
who know this book...
I've applied to five different universities (UK) and have started to receive offers. I'm having a hard time to decide which of the university to choose, as before applying I always had the idea in my head that your mathematics education doesn't really matter, and if you're good at maths then you...
I am an electrical engineer who is fascinated by mathematics. As you might expect, electrical engineering uses a lot of advanced concepts in mathematics from differential equations, linear algebra, calculus, complex analysis etc. However I would like to continue reading maths on my own.
I would...
Hi,
So I am trying to show the following:
##(A \cup B)\sqcup(A \cap B) \leftrightarrow A \sqcup B##
The proof that I am trying to understand starts with:
##A \leftrightarrow (A \backslash B) \sqcup (A\cup B) \qquad (1)##,
and
##A \cup B \leftrightarrow (A\backslash B)\sqcup B \qquad...
Hello all,
I'm a physics and math undergrad and I'm having a very difficult time deciding between these two programs. Fortunately I was accepted into both, so it's a good problem, but having to decide between the two is starting to wear on me; I really love both programs. I've gotten great...
What kind of mathematical disciplines/fields take part in what's called "applied mathematics"?
As far as I know, it's Differential Equations, Calculus, Statistics and Linear Algebra. What other fields are there? I'm sure there are some others.
Hello.
I am taking intro to modern physics and optics next semester, the intro to modern physics is a 300 level class and the optics course is a 500 level class, at Wayne State University.
I want to come into next semester very well practiced in the math needed for those classes.
Could...
Hi all,
I came across the Budapest Math Semester and was wondering what people think of it? One of my profs has heard good things from faculty, but neither of us have been able to locate a student from our university to talk to. The idea of doing a summer session sounds awesome as well. I...
I am a musician, I've been playing guitar form 8 years now. And piano and drums as well for under 3. People tell me music is mathematical same with artwork, something i am also very proficient at. Is it purely from the patterns of the notes and timing of the pitches that make it mathematical? Or...
Okay, so, I'm about 2 semesters from completing my AA degree and I decided a couple semesters ago that I really want to be a math major. I am not a traditional student exactly - I was homeschooled and my math education was not strong, so I ended up placing into Intermediate Algebra in my first...
I graduated from high school this year and took the three main sciences (biology, chemistry and physics) as well as math up to Calculus.
I've decided to take a year away from school for a couple reasons. But that doesn't mean that I must stop learning.
Recently I bought a book which gives...
Dear friends,
I'm presently a junior math undergraduate, and my ultimate goal is to do my master's/PhD work in quantum mechanics, specifically exploring possibilities of temporal superposition for advanced quantum computing.
The question is if it is doable to go from a bachelors in...
I tried doing a google search on this and couldn't find the information I was looking for.
My first undergrad was in Intelligence Analysis (I was MI in the Army) and now in my 4th year as a Business Student and I've gotten the math bug. I'd like to avoid high costs of school (my current...
Hi all.
I am a first year freshman in B.Sc Physics and i am wandering that what fields in mathematics that is required for us to become a theoretical physicist?
As i know calculus is the fundamentals of physics,right? O.o
Correct me if i am wrong. Thank you :smile:
Which branch of statistics and mathematics deals with extrapolations and trend analysis? That is, where one can estimate various trends (be they exponential, linear, etc.) that apply to our data and draw a trend which could extrapolate the future variation.
Am I referring to the time series...
I'm thinking of applying for a degree in engineering at university next year and was wondering, what is the most commonly used mathematics that you engineers everyday in your jobs?
I have only taken mathematics up to trig and I was curious if I would be able to start reading books on more advanced topics like Abstract Alegebra and topology??
Hi there,
Im looking for a theorem that relies on the axiom of choice, but is used in applied mathematics (economics, physics, biology, whatever). In other words a mathematical theory we use to say something about the real world.
This is because I'm wondering if discarding the axiom of...
I'm studying engineering at the moment and within the degree there is only 3 compulsory courses of maths. I love maths and would like to get a bachelor of mathematics but I was wondering how useful it would be to a job in engineering.
Thanks in advance for the advice.
Masters before Phd in Mathematics --bad idea?
Hi all,
I am a senior at a regional campus of a large state university in the US. I have always thought that since I love math (and I do really love learning and doing math), that love of the subject would be enough to propel me through a PhD...
A funny thing happened to me recently...
I solved a complicated math problem (for me anyway), and it was almost as if I had no idea of what I was doing. I just started writing... and it kind of came out, unconsciously...
I think I know why Poincare said that intuition creates while logic...
"Mathematics is the gate and key to the sciences", Robert Bacon said. That statement is as relevant today as it was 800 years ago. Human culture changes but mathematics is forever. Mathematical beauty will be as relevant to mathematicians and poets today as it was thousands of years ago. Surely...
I plan to study from Peskin and Schroeders book if it helps, I just need to know what topics I need to study and it would be greatly appreciated if someone could tell me what books are good on the subject, I have a limited budget however and if I could get a single or only 2 or 3 books covering...
Do you think that matter, energy, space, time, etc. are discrete, or continuous?
If they are discrete, is continuous mathematics limited to a very, very good approximation for modeling physical phenomena?
Hello all,
A brief history is that as a child (I'm only 26 now) I had performed poorly at Mathematics and it wrecked my confidence. I had no interest in long division, basic algebra etc and focused elsewhere because I never viewed it as a means to an end. Suffice to say I suffered a bit of Math...
Just like calculus (single as well as multi-variable) and linear algebra are not only useful but really similar to classical mechanics. What are the branches of mathematics that I need to know in order to have that same feeling of deja-vu when studying electricity/magnetism and waves/optics? I...
Hello everyone!
As the title of this thread possibly suggests to you, I'm not very skilled with mathematics. I would like to say I don't blame my teachers, I'm not insinuating that by any means. What I'm hoping to find is a book that can teach me "from the ground up" (the basics to calculus...
Hello, I am currently in my final year at a California State University majoring in Mathematics (Applied track) and minoring in computer science. I've begun lurking forums such as the physics to figure out what sort of programs I am qualified to apply for, and what be good opportunities as well...
I'm interested in mathematical or theoretical physics (and, I am quite aware of how daunting it is to obtain a career in this field). I'm curious, if I do research with the mathematics department, does this look good?
Currently I might have a project in dynamical systems, although I could...
My question is kind of simple, does the calculus of variations find its way into the design of the shape of an airfoil?
I'm interested in what kind of mathematics gets used in basic airfoil design. I suspect the calculus of variations must be involved, but I know nothing about deriving the...
Hello,
First of all i found too much helpful posts at physicsforums to understand many things and basic principles about the majors of Engineering, Physics and mathematics.
I got recently B.Sc degree in Electronics and Communication Engineering and that was good now i decided to have a...
Hello,
First of all i found too much helpful posts at physicsforums to understand many things and basic principles about the majors of Engineering, Physics and mathematics.
I got recently B.Sc degree in Electronics and Communication Engineering and that was good now i decided to have a...
Hey guys, the title basically says it all! I'm looking for a book to work along side Serge Lang's basic Math's book. Something which goes into topics more in depth. I'm out of scratch with my Math's :(
Hope someone can point me to a good text!
Luke
(I know this has been discussed extensively, but please read my situation.)
Hello,
I will be a college freshman in this fall to begin my studies in the sciences. I have equal passion for both subjects so I am going to choose whichever I am better at. I have seen a number of threads in this...
How do you think of numbers when you're doing math? I particularly feel like sometimes we get to close to acting like computers. We just scan through a list of symbols and compute another list of symbols that makes sense in a certain context. We hardly ever think of things concretely and how...
Homework Statement
Problem 1:
If A is an m x n matrix and Ax = 0 for all x ε ℝ^n, prove that A = O.
If A and B are m x n matrices and Ax = Bx for all x ε ℝ^n, prove that A = B.
(O is the 0 matrix, x is the vector x, and 0 is the 0 vector.)2. The attempt at a solution
First off, I understand...
I'm planning on taking a computer science course this fall on Theory of Computation. However, one of the prereqs is "experience in formal mathematics at the level of [course on Discrete Mathematics]." I've done a little bit of discrete math before (The Art of Problem Solving covers some discrete...
Homework Statement
Hello.
Here is the question:
Determine whether or not R is some sort of order relation on the given set X.
X = {∅, {∅}, {{∅}} } and R ε ⊆.
I can't seem to figure out why the ordered pairs given are what they are.
Homework Equations
None.
The Attempt at...
Homework Statement
A persons desire to eat is inversely porportional to a persons desire to not eat. The problem is I don't know how to write this down mathematically. Let's give a value to someone's desire to not eat after 3 days [40], that persons desire to not eat is going to be [-40]...