In order to gain a minor you must gain a total of 10 points from the learning projects, or a combination of learning projects, research, and/or instructional design.
In order to gain a major you must gain a total of 20 points from the learning projects, or a combination of learning projects, research, and/or instructional design.
These are courses designed for those who do not feel up to beginning with calculus.
The natural numbers, addition, subtraction, integers, multiplcation, division, word problems, factors/multiples/and divisors, rational numbers, and decimals.
Approximate results with decimals, powers, roots, real numbers, imaginary and complex numbers, logarithms, ratio and proportion, numerical sequences, graphing numbers, and percentages.
Algebraic symbols and expressions, doing arithmetic with symbols, simplification, symbolic sequences, series, symbolic ratio and proportion, polynomial expressions, factoring polynomials, rational expressions, and radical expressions.
Equations and their solution, inequalities, simple equations, simple inequalities, quadratic equations, quadratic inequalities, deriving equations and inequalities, algebraic word problems, cubic equations and inequalities, and quartic equations and inequalities.
Plane figures, dimensions and areas of plane figures, common geometric constructions, solid figures, dimensions/surface areas/and volumes of solid figures, the Cartesian plane, points and lines on the Cartesian plane, algebraic properties of lines, plotting equation curves on the Cartesian plane, and plotting inequalities.
Systems of measurement, denominate numbers, scientific notation, word problems involving measurement, tabulating data, graphing data, averages, other measures of central tendency, measures of dispersion, and error in data.
Propositions/connectives/and truth tables, implication, rules of logic, direct proof, reductio ad absurdum, proof by cases, sets and subsets, set operations, significant proofs of arithmetic/algebra/and geometry, and proof by mathematical induction.
Properties of lines, angles, triangles, congruence, polygons, area, circles, constructions, solid figures, and surface area and volume.
The concept of a function, plotting functions, properties of the line, plane vectors, properties of the circle, properties of the conic sections, parametric equations, polar coordinates, solid analytic geometry, and spatial vectors.
The idea of relations, functions, algebra of functions, graphs of functions, algebraic functions, polynomial functions, rational functions, the fundamental theorem of algebra, exponential functions, and logarithmic functions.
Two equations in two unknowns, one equation and one inequality, two inequalities, three equations in three unknowns, Gaussian elimination, matrices, converting a system of equations into a matrix equation, matrix inversion, determinants, and solving systems by determinants.
Angle measurement and the unit circle, circular functions, trigonometric functions for significant angles, graphs of trigonometric functions, major trigonometric identities, using the identities, inverse trigonometric functions, the law of sines and the law of cosines, vectors and trigonometry, and complex numbers and trigonometry.
This is a short learning project designed to provide the practical basis for future development in the study of pure or applied mathematics. This not not a project to develop mastery of the facts of mathematics, rather it is designed to expose basic techniques for the discovery of facts. This project is only six lessons long: What is mathematics? How do we study mathematical systems? What can we learn from mathematical structures? How can we learn to apply mathematical structures? What are some projects to get started in mathematics? What are some open problems in mathematics?
Logic, proofs, basic set theory, relations, functions, countable and uncountable sets, theory of algebra, theory of groups, limits, and theory of analysis.
This project is under development.
Theory of limits, continuity, the derivative and differentiability, the derivatives for basic arithmetic operations, the chain rule, trigonometric functions, exponential and logarithmic differentiation, parametric differentiation, higher-order derivatives, and partial derivatives.
This project is under development.
Problem-solving strategies, related rates, extreme values of functions, optimization, curve sketching, numerical differentiation, the linear approximation, the mean value theorem, Taylor's theorem, and Newton's method.
Substitution, integration by parts, integration by partial fractions, trigonometric integrands, trigonometric substitutions, other substitutions, differential equations, geometry, centroids, and scientific applications.
This project is under development.
This project is under development.
This project is under development.
This project is under development.
This project is under development.
This project is under development.
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