Of the original seven Millennium Prize Problems set by the Clay Mathematics Institute , six have yet to be solved, as of 2016: [10]

The seventh problem, the Poincaré conjecture , has been solved. [11] The smooth four-dimensional Poincaré conjecture —that is, whether a four-dimensional topological sphere can have two or more inequivalent smooth structures —is still unsolved. [12]

Discrete mathematics is the branch of mathematics dealing with objects that can assume only distinct, separated values. The term discrete mathematics is therefore used in contrast with continuous mathematics, which is the branch of mathematics dealing with objects that can vary smoothly (and which includes, for example, calculus ). Whereas discrete objects can often be characterized by integers , continuous objects require real numbers.

The study of how discrete objects combine with one another and the probabilities of various outcomes is known as combinatorics. Other fields of mathematics that are considered to be part of discrete mathematics include graph theory and the theory of computation. Topics in number theory such as congruences and recurrence relations are also considered part of discrete mathematics.

Through online tutoring and homework help offered by TutorVista, students can improve their grades and boost up their confidence. We help you to solve problems based on Set theory, Graph theory, Number theory, Logic, Permutations and Combinations with ease. Discrete Mathematics is the single most important field of Math hence our excellent online tutors have expertise in all the relevant Math topics. The topics included in the study of discrete math are mentioned below:

Answer: Let the women be denoted by W and the men be denoted by M.

,$M_1$, $M_2$, $M_3$, $M_4$, $M_5$, $M_6$,

Now the women can sit at the places marked by ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''.''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''.

We have seven places for 5 women. The women can sit in $^{7}\textrm{P}_{5}$ ways. Also 6 men can be arranged in 6! ways.

$\therefore$ Total number of arrangements = 6! $\times$ $^{7}\textrm{P}_{5}$ = 1814400

Smale''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''s problems are a list of eighteen unsolved problems in mathematics that was proposed by Steve Smale in 1998, [1] republished in 1999. [2] Smale composed this list in reply to a request from Vladimir Arnold , then vice-president of the International Mathematical Union , who asked several mathematicians to propose a list of problems for the 21st century. Arnold''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''s inspiration came from the list of Hilbert''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''s problems that had been published at the beginning of the 20th century.

There are many unsolved problems in mathematics. Some prominent outstanding unsolved problems (as well as some which are not necessarily so well known) include

13. Lehmer''''''''''''''''''''''''''''''''s Mahler measure problem and Lehmer''''''''''''''''''''''''''''''''s totient problem on the existence of composite numbers such that , where is the totient function.

Problems of the Week

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The University of Central Florida Mathematics Education Program hosts a math problem of the week contest. Different problems for elementary, middle, and high school.