Explore sequences and recurrences, solve common problems in combinatorics and compute properties of graphs and lattices. Compute a possible formula and continuation for a sequence:. Analyze a graph specified by adjacency rules:. Analyze functions and expressions containing imaginary numbers or complex variables.
Compute properties of a function of a complex variable use the variable z:. Compute the residue of a function at a point:. Perform numerical analysis and optimization of systems and objects, including packing and covering of objects and control systems. Numerically integrate functions that cannot be integrated symbolically:. Evaluate Boolean logic expressions and expressions involving sets and set operators. Examine the properties of mathematical functions, such as continuity, surjectivity and parity.
Utilize notable special functions or number theoretic functions. Do computations with special functions:. Do computations with number theoretic functions:.
Gather information about famous problems, conjectures, theorems and paradoxes. Learn about them and their formulators. Get information about a mathematical conjecture:.
Get historical information about a theorem:. Compute; learn about algorithms, definitions and theorems involving; or find properties of continued fractions.
Find the continued fraction representation of a number:. Find definitions of continued fraction terminology:. Find continued fraction papers by author:. Compute properties of datasets, perform statistical inference or model data.
Work with probability distributions and random variables. Calculate basic descriptive statistics for a data set:. Find the sample size needed to estimate a binomial parameter:. Compute the probabilities of certain events occurring. Compute joint, disjoint or conditional probabilities and apply them to real-world situations.
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