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- Are you "struggling" with mathematics?
- Do you want to improve your grade in math?
- Do you want to take your math tests with greater confidence?
- Do you want to make math more fun?
- Are you already scoring an “A” in math but want to learn even more, so that you can be fully prepared for the next higher level of instruction?
- Are you at (or near) the head of the class and feeling unchallenged?
- Do you want to make math more fun?
If you answered “yes” to ANY of the above questions, then you should consider a math tutor. We'll spend an hour or two each week working and playing with math concepts, discussing mathematical principles, and focusing on any uncertainties or difficulties that you are having. There will be an emphasis on having fun, so puzzles and games, and real-world problems, will be used as instruction tools. No homework will be assigned.
Struggling students will improve their grades. Students who are currently “making the grade” will be more confident regarding their abilities and will be fully prepared for “honors” level instruction. High School students will be prepared for pre-calculus and calculus instruction, and will be in position to confidently pass their AP tests.
ALL students are fully capable of high academic achievement. However, many students are not confident in their abilities. It is my goal to increase each student's ability to understand the material and to learn effectively. Mathematics is not "difficult" if it is approached the right way. Anyone with the desire can learn algebra, trigonometry, and calculus if each concept is simplified.
Tutor: Dr. Andrew G.
B.S. Civil Engineering, Carnegie-Mellon University
M.S., Ph.D. Environmental Engineering Science, California Institute of Technology (Caltech)
Dr. G.'s qualifications include a Ph.D. in engineering from CalTech (including a minor in numerical methods/applied math) and over 25 years experience as a practicing environmental engineer/scientist. In addition, he has a lifelong passion for mathematics and, in addition to tutoring all grade levels in math, has volunteered for 6 years in the local public schools in San Rafael (including mathematics instruction and Odyssey of the Mind coach). Dr. G. has a daughter who is currently in high school. He enjoys music, hiking and geocaching.
Dr. Andrew G. has a Ph.D. from Caltech in environmental engineering science with a minor in numerical methods. In addition he has over 30 years experience as a practicing atmospheric scientist and dispersion modeler.
The concepts of Linear Algebra are at the heart of (1) numerical methods (used to develop and evaluate solution techniques that are used by computers to solve large numerical systems such as finite element analyses), (2) numerical solutions of overdetermined systems (i.e., "least squares" which are used in atmospheric receptor modeling techniques such as the Chemical Mass Balance model), and (3) statistical models (correlation and multiple regression).
Dr. Gray's research in air pollution includes the use of meteorological and dispersion computer models which involve numerical solutions of large linear (and non-linear) systems. Dr. Gray has also worked with (and helped in the development of) receptor models such as the Chemical Mass Balance Model and other related multivariate factor-analysis techniques. In addition, he has developed computer programs for the efficient (and stable) solution of linear systems (using such methods as Gram-Schmidt orthogonalization).
Topics in Linear Algebra include:
* Systems of Equations and Matrices - Systems of Equations, Row-Echelon Form, Reduced Row-Echelon Form, Gaussian Elimination, Gauss-Jordan Elimination, Matrices, Matrix Arithmetic, Transpose, Inverse Matrices, LU-Decompositions.
* Determinants - The Determinant Function, Properties of Determinants, Method of Cofactors, Determinants by Row Reduction, Cramer's Rule.
* Euclidean N-space - Vectors, Vector Arithmetic, Norm, Dot Product, Cross Product, Projections, Euclidean N-space, Linear Transformations.
* Vector Spaces - Vector Space Axioms, Subspaces, Span, Linear Independence, Linear Dependence, Basis, Dimension, Null Space, Row Space, Column Space, Inner Product Spaces, Orthogonal/Orthonormal Basis, Least Squares, QR-Decomposition, Orthogonal Matrices.
* Eigenvalues and Eigenvectors - Eigenvalues and Eigenvectors, Eigenspaces, Diagonalization, Jordan Canonical Form.
Very thoughtful, thorough and patient. — Andy has worked out very well for our son. He is thoughtful, thorough and patient. ...
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