What is Mathmatics: Definition and 14 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.

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  1. Ziek_4790

    Discrete Mathmatics :logically equivalent

    1. Consider the statement S =[¬(p ->q)]V[¬(pVq)]. (a) Construct truth tables for S. (b) Find a simpler expression that is logically equivalent to S.
  2. P

    Classical Comprehensive books about the history of physics/mathematics

    I am in search of one or more books that describe the progress in the field of physics (especially during the 18th 19th and 20th century) not only by mentioning the names of lead scientists and the abstract of their work but also have some deeper insights if possible (some math too) last but not...
  3. E

    Programs Advice on majoring in physics and more

    Hello my names Ethan, I am a senior in high school and i plan on attending West Virginia University the coming fall of 2017. I want to acquire a PhD in nuclear physics and also I've been reading about, I believe the name is a complementary degree, other degrees to go along with nuclear physics...
  4. mpoli

    Linear Programming Case Study - Case Problem

    Homework Statement Linear Programming Case Study - Case Problem ( Page # 109 Decision making methods) “The Possibility” Restaurant? In the case problem, Angela and Zooey wanted to develop a linear programming model to help determine the number of beef and fish meals they should prepare each...
  5. infinite.curve

    Resources For Real Analysis and Concepts of Mathmatics

    I have been browsing the web, and I notice that I could not find any websites that have real analysis text around. Yes, I understand that I should look for books written by professionals in the field, but I do not know which one I should buy. Do you know of some online resources to real analysis...
  6. Gadgett

    What can I do with an Associate's Degree in Mathmatics?

    I really need some help. I've spent the past 20 years shooting for my dreams. I got an associates in Electronics and a BA in Graphic Design. Needless to say the past 20 years have yielded no fruit. It's been 10 years since I've gotten my BA and I've never been able to use it. So basically it's...
  7. Zeedr

    Is this idea remotely possible in the distant future?

    Hello, I was just brainstorming for futuristic inventions with context for a sci-fi, high fidelity game (because I'm too cool to revise for exams) - and I thought of one, but my physics and engineering knowledge is at best sketchy when it comes to gravity and nuclear fusion combinations, I was...
  8. T

    Water feature design - pump mathmatics

    Hey everyone, as part of a university project working on renewable energy sources in the garden I am performing some simple fluid dynamics analysis to calculate the pump power needed to feature in this garden water feature. I have designed the schematics of the feature and worked out the...
  9. J

    Fair fax county mathmatics league

    Ah... This problem is very interesting. but,, I don't know how to solve it... T,T "If a<b, what are both ordered pairs of integers (a,b) which satisfy a ^b = b ^ a ?"
  10. S

    Programs Theoretical mathmatics for physics phd

    hey everyone, If I plan to pursue a physics phd in quantum theory/string theory do you recommend I get a B.S. in theoretical mathematics as well (with linear pde, Fourier anal, and topology, etc.)? I'm still not sure whether applied or theoretical math is the better choice.
  11. M

    Name that Mathmatics term (Periodic blank )

    Name that Mathmatics term (Periodic "blank") I have no idea what the english term for it is. As a result it is more-or-less impossible to find something about it online. One can give the equation for a sine kurve simply by looking at the graph, taking values such as the amplitute, period...
  12. T

    Mathmatics Needed: Learn Special & General Relativity

    I was just wondering if anyone is able to give me a list of mathmatical areas that i will need to learn before i am able to start to learn about the special and general therories of relativity?
  13. wolram

    Is Math the Key to Unlocking Our Potential?

    An article i came across, i thought may be of some interest. http://www.sciencenews.org/articles/20060304/mathtrek.asp