I have been tutoring all levels of math for over 7 years now. I really enjoy math as a subject, and try to impart the fundamental concepts of math rather than trying to just teach the algorithms. Math really should be about understanding the logic behind it and less about route processes (we have computers for that). A bit about me. I currently do tutoring and statistical consulting full time. I worked at a Fortune 500 tech company for almost 2 years (doing math and statistics) but really e... [more]
Algebra II is the basis for all future math course because it leads to trigonometry, pre-calculus, and calculus which leads to even higher math. So a solid understanding of Algebra II is essential. Algebra II covers many topics, including solving systems of equations, graphing functions, inequalities, absolute values, complex numbers, polynomials, exponents, radicals, logarithms, conic sections, and sometimes basic statistics, combinatorics, matrices, sequences and series.
Calculus is the basis for all of higher mathematics and hence it is important to have a good fundamental understanding of it for anyone going into higher math or the sciences. Calculus is the study of infinitesimals and what happens to things as you take the limit to infinity. Basic calculus involves learning limits, derivatives and integrals. As the student masters these he or she moves onto multi-variable calculus which involves vectors, 3-d graphing, dot products, cross products, and much more. Additional topics include sums and series, basic differential equations, and applications.
Geometry involves the study of shapes, sizes, and relative positions. In high school geometry students study lines, parallel lines, triangles, circles, and angles. This is often a students first introduction to proof and many find this to be quite difficult since they are used to dealing with numbers and not abstract concepts. There are lots of theorems to know but with a good understanding of why these theorems work students can find the subject much easier.
Private tutor at all levels (high school, college, graduate school and MBAs) of statistics for 8+ years. Data Science and Statistical consultant to small and mid-sized companies. I know statistics inside and out to help you with all the details.
A differential equation is an equation which has the function, it's various derivatives, and one or more independent variables. The objective is to find the general function that matches the equation. Once this is done particular solutions can be found using from initial conditions. The easiest differential equations to solve are usually linear, however separable, homogeneous, and exact can also be fairly straight forward. The method of integrating factors can be useful in solving differential equations as can series solutions. Differential equations are highly applicable, especially in modeling. I have taken several differential equations classes during college including, differential equations, ordinary differential equations, and partial differential equations.
The study of Linear spaces. Linear models are some of the most basic models to learn but are also some of the most useful. Linear algebra includes the study of vector spaces(looking at the difference between dependent and independent vectors, column space, row spaces, null space, etc.), linear transformations (often in the form of matrices), and the invertible matrix theorem. Since matrices are a big part of linear algebra, matrix determines, eigenvalues and eigenvectors are essential. Finally, Linear Algebra has many applications include it's use in linear regression (for multiple variables), and solving systems of differential equations (quite useful for modeling).