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Elementary Math
Do basic arithmetic. Work with fractions, percentages and similar fundamentals. Solve place value and word problems.
Do exact arithmetic with fractions:
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Algebra
Find roots of and expand, factor or simplify mathematical expressions—everything from polynomials to fields and groups.
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Calculus & Analysis
Compute integrals, derivatives and limits as well as analyze sums, products and series.
Solve an ordinary differential equation:
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Geometry
Compute the properties of geometric objects of various kinds in 2, 3 or higher dimensions. Explore and apply ideas from many subfields of geometry.
Compute properties of a geometric figure:
Plot a conic section and identify its type:
Compute properties of a polyhedron:
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Differential Equations
Solve differential equations of any order. Examine solutions and plots of the solution families. Specify initial conditions to find exact solutions.
Solve a linear ordinary differential equation:
Solve a nonlinear equation:
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Plotting & Graphics
Visualize functions, equations and inequalities. Do so in 1, 2 or 3 dimensions. Make polar and parametric plots.
Plot a region satisfying multiple inequalities:
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Numbers
Work with various kinds of numbers. Check for membership in larger sets, such as the rationals or the transcendental numbers. Convert between bases.
Compute a decimal approximation to a specified number of digits:
Convert a decimal number to another base:
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Trigonometry
Perform trigonometric calculations and explore properties of trigonometric functions and identities.
Compute values of trigonometric functions:
Solve a trigonometric equation:
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Linear Algebra
Explore and compute properties of vectors, matrices and vector spaces.
Compute properties of a vector:
Calculate properties of a matrix:
Determine whether a set of vectors is linearly independent:
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Number Theory
Analyze integers; subsets of the integers, including the prime numbers; and related ideas.
Compute a prime factorization:
Solve a Diophantine equation:
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Discrete Mathematics
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:
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Complex Analysis
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:
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Applied Mathematics
Perform numerical analysis and optimization of systems and objects, including packing and covering of objects and control systems.
Minimize or maximize a function:
Numerically integrate functions that cannot be integrated symbolically:
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Logic & Set Theory
Evaluate Boolean logic expressions and expressions involving sets and set operators. Solve Boolean equations. Compute truth tables. Generate Venn diagrams.
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Mathematical Functions
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:
Find representations for a function:
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Mathematical Definitions
Make queries about various definitions and descriptions in mathematics.
Find information about a math concept:
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Famous Math Problems
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:
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Continued Fractions
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:
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Statistics
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:
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Probability
Compute the probabilities of certain events occurring. Compute joint, disjoint or conditional probabilities and apply them to real-world situations.
Compute the probability of a union of events:
Compute coin‐toss probabilities:
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Common Core Math
Get information about math Common Core Standards for kindergarten through eighth grade.
Evaluate an expression (CCSS.Math.Content.6.EE.A.2c):
Perform multiple operations with rational numbers (CCSS.Math.Content.7.NS.A.2c):
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