# Calculus

Calculus I: Review Problems I: Limits, continuity, derivatives, and tangent lines. A handful of solved problems.

Calculus I: Review Problems II: Riemann sums, definite integrals, antiderivatives (minor editorial corrections have been added)

Calculus II: Developing intuition for using integration techniques: a detailed analysis of various problems on antiderivaties

Calculus I: Review Problems III: Antiderivatives, fundamental theorem of Calculus, areas, volumes, length of curves (minor editorial corrections added)

Calculus I: Review Problems IV: Shell and disk (washer) methods

Derivatives and Tangent Lines: Selected problems solved in detail. An elementary introduction to the computations behind these subjects.

Calculus Problems Solutions: Selected problems solved in detail

# Probability

Classic Probability. An introduction through elementary examples.

Probability Theory. Basic definition and various counting problems.

Confidence and prediction intervals. An brief explanation of the underlying theory behind confidence and prediction intervals.  A few problems for estimating the mean and variance of a population are solved to illustrate it.

# Pre-Algebra

Division Algorithm, roots of polynomials, and factorization

Practice Assignment I: Coordinates and geometry, algebra, exam (SAT) type problems. A variety of problems on these topics, many solved.

Practice Assignment II: Arithmetic sequences, algebra, Pythagorean triples (rational and (some) irrational numbers), exam (SAT) type problems.

Practice Assignment III: Algebra, Functions and Graphs, Euclidean Geometry (from the beginning).

Testing your Mathematical Reasoning: A good set of problems involving basic key concepts. Understanding many of them will indicate that you have a solid background for a college education. Solving many of them on your own will indicate the level of ability you have at this point.

Final Review (solutions)

# STEM Student Development

Mathematical Reasoning: An Overview.  A handful of problems that test thoroughly your ability and preparation for a mathematical college education.

Mathematical Reasoning: An Overview. Additional set of problems involving basic concepts that are part of a solid background for a college education.

Linear Functions: Straight lines, linear functions, and arithmetic sequences.

Absolute Value y=|x|: Broken lines, the geometric median problem, piece-wise linear functions.

# Linear Algebra

Review Problems: Linear Equations, Vector Spaces, Linear Transformations, Determinants, Diagonal Matrices, Elementary Canonical Forms, Eigenvalues, Eigenvectors

(Applied) Linear Algebra Problems.  A handful of linear algebra problems that emphasize the computational aspects of the subject.