Tell some questions on pure mathematics spatially in abstract algebra topology for interview on admission ph.d
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One question in number theory most likely :\n\nfor  all integers a, b, c and n,\n\nprove that :  \n\na^n + b^ n does not equal c^n for n > =3
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Try searching for "Mathematics site:ph"\nYou can replace Mathematics by more specific areas of interest.
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I wasn't there, but currently I am an exchange student in germany. My host sister is studying math there, and she says it's absolutly beautiful. There is the 'Philosopher's Weg' (way) that has a lovely view, the old castel and Altstadt are also really pretty. I'm excited to be going there later in June! Good luck studying there! It's got a great rep and is beautiful to boot!
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http://aleph0.clarku.edu/~djoyce/mathhist/mathhist.html
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sphere, elliptic, plane, euclidean, pseudosphere, hyperbolic
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I can provide you complete programs of data structures (linked list, array handling, stacks, queues, tress, graphs, and other algorithms). for this you have to provide me your information and details for what purpose you have to use this? and what your are doing currently. you can communicate me on my email address. abhi_patni@yahoo.com.
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weezy is on the right track, that glow1989 is on the right track.  For everyone who thinks that writing 1+1=2 is so obvious that it constitutes a self-contained proof of itself(!)... if you undertake a serious study of mathematical proof, you might find that 357 pages is a good length for a quick introduction to the ideas that are involved in considering questions in this area.  Of course, I am talking about actually UNDERSTANDING something - very different to simply passing an exam, regardless of the 'level' of maths you are enrolled in.\n\nYes, as you mentioned, this is a hard question.  'Proving' that 1+1=2 is not as simple as it sounds, because of the inherent question of what we mean by 'prove'.  You might have noticed that some proofs you have used depend on other proofs, which in turn depend on other proofs, ... which ultimately rest on a handful of axioms.  It is the nature of operations that are allowed by any axiomatic system, that determine the characteristics of mathematical problems that can be said to be SOLVABLE.  It is no small task to understand the axioms that underlie our systems of mathematics.  For example, maths students learn: that division by zero is undefined; that any object raised to a null power is equal to unity; some differences between rational and irrational numbers; what we mean when we consider objects to exist in 'sets'; and so on.  Those who consider themselves to be excellent students are usually able to list these rules in rapid-fire style.  But if we are asked to 'prove' why those rules are the way they are, the questions start to seem fuzzy, and you typically run out of convenient formulas to rely on.  You could easily write 357 pages just to explain what you actually MEAN by the numbers 1 or 2, without worrying about the definition of the addition operation!  As usual, people might do better to stop and consider what the question is asking before booting in a smug answer.\n\nLook into Hilbert's Problem (David Hilbert - German mathematician), which was a more workable and compact form of a proposal by Russell and Whitehead to formalise mathematics on a general basis, according to well-established axioms and procedures.\n\nOther notable mathematicians to work in this area were Alan Turing, Alonzo Church (look for Church's Lambda Calculus), Emil Post, and the brilliant Kurt Gödel.  In more recent decades, look for Gandy (1988) and of course many others.\n\nLol, molawby is spot-on.  I wish he'd posted b4 me... would've saved me a bit of typing.  If all you need to do is learn to sing the right song, to pass your exams and get the job that stipulates that you need to have completed such-and-such a course, then you don't have to worry about any of this.  Of course, that doesn't mean you have to dismiss it either.  But if you are chasing a deeper understanding, it probably does take the 20 yrs, and you won't necessarily get paid for it, heheheh.\n\nFor bedside reading, I suggest Roger Penrose etc...
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Isomorphic if you are in abstract algebra.\n\nCongruent if you are in geometry.
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go online, click on search and type in MATH 012 : Intermediate algerbra course. something should pop up. and then write down the evidence
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Analytic and Algebraic Number Theory contain easily stated theorems with extensive wide-spanning proofs that require knowledge from almost every area of mathematics, including topology and category theory. As such, I would say this area of study is the most difficult, as one that requires the most mathematical experience to tackle. \nAlgebraic topology, on the other hand, can easily be taught in its basic form to motivated high schoolers. It doesn't even require knowledge of calculus, though such knowledge enriches the subject when one gets to cohomology and applications to vector fields and differential equations. These topics can be saved for a college course.
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Here are some topics you could try:\nVedic Mathematics\nPolynomials\nLinear Equations\nNumber Systems\nLines and Angles\nQuadrilaterals\nAreas\nTriangles\nSurface Areas\nVolumes
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First the questions must be transfored to my space:\n\nWhat should you have for dinner tonight?\nHave I seen the movie Proof?\nHow do I revolutionize Mathematics?\n\nThen the questions must be generalized to n dimensional space:\n\nWhat should we have for dinner tonight?\nHave we seen the movie Proof?\nHow do we revolutionize Mathematics?\n\nSo using generalized anti-question transform matrix obviously the answer is:\n\n[We have seen proof of revoloutionalized mathematics for dinner , Dinner should do the movie tonight , 0 , more DON is needed for KEY]\n\nNote that last answer do not satisfy main equation, and 0 is axiomatic solution.
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http://mathforum.org/dr.math/\n\nThis is a good site where people ask questions and the questions are answered by volunteer professors.  May not have pictures but there are very good explanations.
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I am a math major so I have taken every math class. Start with Elementary Statristics...it is not that bad mostly pie and bar graphs for the first half of the semester.
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As for math, I'd recommend mathworld.  I don't know about other specifically.  It is not the most readable, but it's a good enough resource for graduate students.
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http://www.pd.org/topos/perforations/perf7/koresh/nash-koresh.html
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mathworld \n\n\n\n--- LeeeN