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### krishnapal singh

Discussion -What is the difference between these lines-

(i) there exists x in set of real no. ,for all y in set of real no such that x+y>0

(ii) for all x in set of real no., there exists y in set of real no. such that x+y >0

(i) there exists x in set of real no. ,for all y in set of real no such that x+y>0

(ii) for all x in set of real no., there exists y in set of real no. such that x+y >0

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thanks

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### David Kotschessaowner

Modern History - In 1900, David Hilbert published a list of twenty-three open questions in mathematics, ten of which he presented at the International Congress of Mathematics in Paris that year. Hilbert had a good nose for asking mathematical questions as the ones on his list went on to lead very interesting mathematical lives. Many have been solved, but some have not been, and seem to be quite difficult. In both cases, some very deep mathematics has been develop...

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Refurio Anachro

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Wonderful article! After a long time shaking my head at people still trying to solve the continuum hypothesis, a few years ago, I started to very slowly change my opinion to: perhaps that might still happen!

During that time, one or perhaps a few hunches have sneaked in and I'd like to check if they even make sense (are answered in the literature, etc...), but I haven't managed to capture my ideas in proper questions.

[Edit: So I might ask people to talk me out of it. My feeling clearly says that there's something I don't understand. Phew, I almost forgot that this is dangerous territory.]

Logic is subtle and quite complicated. I really like the outlook at the end. Two front lines, and a dazzling result asking to change the rules.

During that time, one or perhaps a few hunches have sneaked in and I'd like to check if they even make sense (are answered in the literature, etc...), but I haven't managed to capture my ideas in proper questions.

[Edit: So I might ask people to talk me out of it. My feeling clearly says that there's something I don't understand. Phew, I almost forgot that this is dangerous territory.]

Logic is subtle and quite complicated. I really like the outlook at the end. Two front lines, and a dazzling result asking to change the rules.

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### Nosheen Akhtar

Early History -What is the history behind sine,cosine and tangent in math?

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+MichaelKingsfordGray thanks

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### Landon Azbill

Modern History -Much of the maths that I've learned about up to this point was developed as late as the mid 20th century, and as far as I know there haven't been any major developments in the 21st century that aren't just proofs of things conjectured in previous centuries. So I'm curious if anyone here knows of or could point me in the direction of any 'new' maths (new meaning not just a proof of some preexisting conjecture(s)) developed around or in the 21st century.

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David Kotschessa

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+Landon Azbill

Well, this is what I love about combinatorics. Math teachers are fond of telling students how concepts build on another and how we must master one subject before we can understand the next. Combinatorics is different. You can teach combinatorics concepts to someone without any algebra or set theory, but clearly algebra and set theory are tools or languages that can be applied to tackle and communicate combinatorics problems.

Colleges will often list "prerequisites" to combinatorics and graph theory classes, but these are so much prerequisites as a "mathematical maturity" requirement. There's no need of calculus in Combinatorics, but time spent wrangling with slightly harder or more abstract math will make the topic less intimidating.

The topics you've taken are great preparation in that sense. In statistics, you've already done some combinatorics, because doing statistics requires counting things. In particular, if you had any discussion on probability, you probably used the binomial coefficients (n choose k) in which case you were doing basic counting.

Now, if you want to tackle the most

But even my graduate level combinatorics book provided a review of the necessary chunks of those topics (which of course, my professor left us to cover in our own time) before we used them. So it's not like you were expected to have mastered linear algebra and probability. I learned more probability doing combinatorics than I did in probability!

Anyway, that's a bit more than you asked for. I wish I could recommend you a good book. Unfortunately I don't feel the books I learned from were something I would recommend to people. They worked with the professor that I had, but he had his own way of approaching the material and skipped around a lot, and provided his own notes, and should really just write his own book. I did like the Springer book for graph theory, and I think they have one for combinatorics also.

Well, this is what I love about combinatorics. Math teachers are fond of telling students how concepts build on another and how we must master one subject before we can understand the next. Combinatorics is different. You can teach combinatorics concepts to someone without any algebra or set theory, but clearly algebra and set theory are tools or languages that can be applied to tackle and communicate combinatorics problems.

Colleges will often list "prerequisites" to combinatorics and graph theory classes, but these are so much prerequisites as a "mathematical maturity" requirement. There's no need of calculus in Combinatorics, but time spent wrangling with slightly harder or more abstract math will make the topic less intimidating.

The topics you've taken are great preparation in that sense. In statistics, you've already done some combinatorics, because doing statistics requires counting things. In particular, if you had any discussion on probability, you probably used the binomial coefficients (n choose k) in which case you were doing basic counting.

Now, if you want to tackle the most

**recent**combinatorics, you will run into proofs that pull from other branches of mathematics. There is a "linear algebra method," a "probabalistic method," and I have seen a few proofs using finite fields (which you would study in abstract algebra).But even my graduate level combinatorics book provided a review of the necessary chunks of those topics (which of course, my professor left us to cover in our own time) before we used them. So it's not like you were expected to have mastered linear algebra and probability. I learned more probability doing combinatorics than I did in probability!

Anyway, that's a bit more than you asked for. I wish I could recommend you a good book. Unfortunately I don't feel the books I learned from were something I would recommend to people. They worked with the professor that I had, but he had his own way of approaching the material and skipped around a lot, and provided his own notes, and should really just write his own book. I did like the Springer book for graph theory, and I think they have one for combinatorics also.

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### Pat Ballewmoderator

Today in History - But just as much as it is easy to find the differential of a given quantity, so it is difficult to find the integral of a given differential. Moreover, sometimes we cannot say with certainty whether the integral of a given qu...

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### About this community

This community is for anyone interested in the history of mathematics from ancient to modern times. Anybody interested in math history at *any* level is welcome.
NOTE: While there are a lot of interesting math memes, jokes, etc. floating around the Internet, we limit our discussion to topics of historical interest. Other posts will be removed.

### Pat Ballewmoderator

Today in History - Thanks for the great memories, Students of Lakenheath Perhaps... some day the precision of the data will be brought so far that the mathematician will be able to calculate at his desk the outcome of any chemical combination, ...

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### Bruce Mincks

Discussion -Let's not confuse the means with "non-contradiction"; the results are absurd.

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### Arindam Bose

Modern History -Did You Know: What really made Italian mathematician Leonardo Pisano so famous?

Visit the post for more.

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Fibonacci is so to be added...

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### Pat Ballewmoderator

Today in History - Mathematics is the most exact science, and its conclusions are capable of absolute proof. But this is so only because mathematics does not attempt to draw absolute conclusions. All mathematical truths are relative, conditiona...

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