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.
Homework Statement
Hey guys I am having a bit of a difficult time with this question, if some one could help me out it would be appreciated, thanks.
Consider the following argument. "If the weather is fine, and the train is early, then the dog will sit on the tuckerbox. The train will be...
From the top of a cliff, which runs North-South, the angle of depression of a yacht, 200 m out to sea and due east of the observer is 20 degress. When the observer next looks at the yacht he notices it has sailed 150m parallel to the cliff. Find:
The angle of depression of the yacht from the...
Hi all,
My husband has a Master's degree in Applied Mathematics and we've been job searching for over 6 months now. Only gotten a couple of interviews and sent out hundreds of resumes. I feel like we're doing something wrong because I've always read/heard that people with this major should be...
What is mathematics books need to read to well understand Quantum Field Theory of Weinberg Vol 1,2,3?Please hint me some group theory books?I know not much in representation of group.
Are there any good first year textbooks which cover first year differential (limits, partial derivatives, intro vector calculus), integral calculus, DEs, AND linear algebra - vectors and matrices.
other stuff like complex numbers, infinite series, etc would be a bonus.
As in a single textbook...
I know physicists are not about analogies. For example there is no real analogy for quantum entanglement or super positions in the real world.
But the problem is that we don't really have a theory for everything now, and relativity and quantum fields are not consistent right?
So could it be...
In your opinion, what is the most difficult written text (e.g. a book or a paper) on mathematics?
My candidate: Principia Mathematica by Whitehead and Russell
http://nautil.us/issue/24/error/in-mathematics-mistakes-arent-what-they-used-to-be
A very interesting article which I think furnishes a point I've been making for a while about mathematics: proofs are as eternal and infallible as the creatures which create them.
EDIT: But with a bit of...
Student's Guide to the Mathematics of Astronomy, by Fleisch and Kregnow.
For beginners, uses algebra, geometry, and trig applied to astronomy and cosmology. Helpful for students who get bogged down in mathematical manipulations and coming up with equations in the first place.
Dear Physics Forum friends,
I am a college sophomore in US with double majors in mathematics and microbiology. My algorithmic biology research got me passionate about the number theory and analysis, and I have been pursuing a mathematics major starting on this Spring semester. I have been...
I am planning to study the following pure mathematics areas (on my own) and wanted to know if this is the best sequence:
1- Formal Logic
2 -Philosophical Logic
3- Sentential Logic
4- Predicate Logic
5- Symbolic Logic
6 -Set Theory
7 -Pure Mathematics (Intro, Pure Math I and II and Hardy) -...
Hello Physics Forums.
So I haven't been on here for a very long time, so hello again.
I am currently a first year at a university in Canada and am to declare my specialization in the coming months. I came into university expecting I'd want to do a degree in physics and astronomy, but over the...
As a quick continuation of the question...what mathematics courses would you (preferably PhD or pursuing a PhD currently) recommend for an undergraduate? I'm interested in high energy/particle physics (I'm working in a lab this summer so we'll see how that goes) and cosmology (no actual...
I'm starting college soon.
2015
Summer
Calculus I and Analytic Geometry
Pre-calculus and Analytic Geometry
Fall
Calculus II and Analytic Geometry
Calculus I for Life Sciences
Linear Algebra
United States History I
United States History II
2016
Spring
Calculus III and Analytic Geometry...
Hello, my name is Diana and I'm studying Electrical and Electronics Engineering. I really love and enjoy Physics so much, and I was planning to study Physics after graduating from Electrical and Electronics Engineering. This is my first semester by the way. The reason I didn't apply for Physics...
I am at starting to become increasingly worried and I need help/advice/what ever you can give me.
My major is mathematics, I will be getting a BS in it next year. I have an interest in Analysis and Probability and will be taking a years sequence in Integration and Measure that year.
My...
Hi guys,
So, I'm a high school senior about to graduate, and because of reasons, I most likely will not be attending a college next year. However, I will apply to colleges next year for a Physics major. In the meantime, I would like to use my time wisely, and I was thinking that the smart thing...
Okay so the name may be bigging it up however i found something in my maths class today that i don't think has previously been published or at least I've never been taught it, it makes converting reacuring decemals a lot quicker
I know about the over 9 rule however acording to my maths teacher...
Hi there!
As you might have already guessed, I'm referring primarily to the 'geometrical' difference (is there such geometry in Hilbert space?) between ##n##-dimensional state vectors
| \psi \rangle = \left( \begin{matrix} \psi_1 \\ \psi_2 \\ \vdots \\ \psi_n \end{matrix} \right)
and their...
Hello! I'm in my final high school year (Bachillerato, as we call it in Spain) and I have to choose between getting a degree in physics or mathematics. Frankly, my uni's approach to physics is far more experimental than theoretical. I do not like that (lol). I love mathematics, and just reading...
I am an economics major with a minor in mathematics. I have three semesters left in college, but if I took an additional semester I could complete a double major in econ and math. If completed, I would be interested in pursuing a master's in applied mathematics. My hope is that this will be...
I'm not going to ask what mathematics are relevant to physics, I know the answer is all mathematics. I was hoping you guys could help me figure out which specific mathematics topics would be best to take concurrently or prior to certain physics topics, so that the order of my classes is most...
Homework Statement
Let A = {1, 2, 3, 4} and let F be the set of all functions from A to A. Let R be the relation on F defined by:
For all functions f, g that are elements of F, (f, g) are only elements of R if and only if f(i) = g(i) for some i that is an element of A.
Let the functions α, β...
I have noticed in the last few months that my interests are moving towards applied mathematics and computing as opposed to engineering. My favorite subjects fluid mechanics, but sadly the aerospace industry is dead (ie, there haven't been many new advances in the last 30 years).
I want to get a...
Hey, I was just wondering what good math periodicals there are out there. I was looking for something that is readable by a wide audience. I've only taken courses in topology, abstract algebra, and real analysis at the undergraduate level. Any suggestions?
Hello,
I am a software professional and 33 years old. I always loved mathematics but never studied/practiced it seriously and forgot whatever I had learned before. One and half years back I started with algebra and then calculus, multivariable calculus and differential equations. All were...
Hello,
First of all, I'm sorry for the long post. I've tried to make it self consistent, but some prior knowledge will be assumed in both physics and differential geometry.
Also maybe some math will be displayed wrongly, it's my first time here...
In physics people usually describe Noether's...
Hey Guys. I'm having a bit of a problem with my solving triangles book. I'm finding the book really easy but there's this one thing that I keep getting wrong. Whenever I'm working with degrees with decimal points my answer aways fluctuates slightly from the real answer. I must be doing something...
I joined this forum recently in the hope that I could get advice on how to start learning Physics and the necessary Mathematics. I also joined in the hope that I could find some like minded people who are also curious about the world. As of now I have no idea about how I will start learning...
I'm about to enter University for a Chemistry major, but I've been throwing around the idea of a double major and also taking Mathematics. They do not offer a physics major, but it's my understanding that physics is heavily reliant on advanced math and that physics itself is so hard because many...
I've been reading an introductory textbook on Mathematical Logic by Richard Hodel, and I often find myself translating the logic into English sentences, or translating it into some other form like a graph that helps me understand what is being stated.
I realize this is probably a very poor...
I was just wondering what people thought about this program. I know a couple of kids who are graduating with their M.S. in pure math from DePaul and they are going to university of Oregon and Toronto for the phd's.
Hello. I am in desperate need for advice. I have searched for advice everywhere and each time failed to obtain it. This is my last resort. Please help me and bare with me while I explain the problem.
I am 28 years old guy. I have literally whole day free to pursue whatever goals I see fit...
Homework Statement
The question is, simplify this equation:
(A ∪ B ∪ C) ∩ ((A ∩ B) ∪ C)
The correct answer is (A ∩ B) ∪ C
Homework Equations
We have been given the commulative, associative, distributive, identity, complement and idempotent laws and DeMorgan's laws, and I researched the...
Hi
I have a bachelor in mathematics, but I just do not know where to go next. The reason I decided to study mathematics was because I have been a puzzle solver since I learned to read (mathematical puzzles, mechanical puzzles etc). So, I wanted to see how I could make a living using that kind...
I recently changed my major to physics from business. I would be going into my senior year as a business student had I stayed, so I have all my core requirements done. While I'm catching up on some maths, I'll need to fill my schedule with electives to remain a full-time student. What courses...
Hi all,
I'm new here and have been studying Physics in my spare time for a couple of years now, but I always just seem to get by in the area of mathematics. Forgive me if I'm looking for something that doesn't exist or on the other hand is very easy to find as I'm not familiar with any of the...
Hey everyone, i just thought i would introduce my self, my name is *removed* I live and study in rural Australia. I am currently studying a bachelor of Civil Engineering and aspire to pursue a matsters in structural engineering. I joined these forums to improve my mathematic skills, seek...
Hello I was looking for a volume set in intermediate/advanced math and I can't seem to find anything. I already have a book in calculus 2 but I'm looking to self study everything after that through advanced math. I want to be a theoretical physicist, but I'm open to learning interesting math...
Hey,
This might be an unusual question, but I'm 20 years old and I really want to study mathematics ; however, I currently am studying for a baccalaureate in law, and I am currently in my second year. Problem is : I absolutely hate law, and wish I had never entered the program in the first...
If we have a simple periodic function (square wave) which can be easily written but the Fourier series is an infinite series of sines and cosines. Why bother with this format when we can quite easily deal with the given periodic function? What is the whole point of dealing this long calculation?
Especially for 2nd & 3rd year courses I'm looking at such as PDEs, Fourier series & laplace tranforms, Vector calculus, intermediate level linear algebra, computational maths, lagranian and hamiltonian dynamics?
Hello Everyone,
I am a young college student that just realized how little of an education I received growing up and attending school in Southern Mississippi. I won't say that it is entirely the fault of my teachers, as soon as I realized I could graduate while barely passing Algebra one I did...
I'm a graduate mathematics student and I did my undergrad in applied math. I also took the normal 10 hrs of physics foundations and then a semester of modern physics (basic quantum intro, special relativity, orbit states etc.). I was thinking about pursuing study in areas that would be...
Hey guys
here is the question i'd appreciate if you could help me with it:
it says that no one dies in planet X,some spies of planet Y were captured by planet X's police.They are so professional that won't say anything to police so their inspection will go on forever and their inspection has no...