### Algebra 1

Algebra 1 generally treats:

* real numbers and their properties as a set

* solving and graphing equations and inequalities, specifically:

* single linear functions

* systems of linear functions

* quadratic functions

* decomposing polynomials into simpler terms (factoring)

* functions involving exponentials and radicals, and

* manipulating rational information (real life problems usually present themselves in terms of ratios of variables or expressions).

I note that students differ in their preferred way of remembering the basic forms of expressions used in algebra -- I'll work with your student to build their recall abilities and techniques, until problem solving becomes routine for them.

### Algebra 2

In addition to covering topics covered in algebra 1, but in greater depth, the algebra 2 curriculum typically includes manipulation of functions of higher degree than 2, solution of systems of equations, and sequences and series.

### Biology

My understanding of biology has been shaped by a lifetime of reading, observing, some teaching and tutoring lately, and much time spent outdoors. For tutoring, I employ semi-Socratic methodology, e.g., "What could evolving life have done if oxygen had not been present to form carbohydrates as energy storage materials?", then "what makes carbohydrates good for this purpose, given the alternatives?" -- when dealing with energy metabolism in aerobes. Though actual experimental manipulations can't be monitored in a tutoring session, the planning of an experiment, use of controls, skills of analysing data and experimental methodological errors, all can be.

### Calculus

Calculus curricula typically proceed from the concept of taking derivatives of functions, and of products of functions, to the reverse process, namely, figuring the integrals of functions and of products or quotients of functions.

Depending on the depth of the course, functions of multiple variables may also be treated, as may integrations of functions involving complex variables. For the most part this is usually a "stand-alone" course, though it may be integrated (so to speak) into physics, chemistry, and statistics courses. I have studied all this in my scientific schooling, and applied it very occasionally, mostly for recreational engineering-type calculations.

I try to incorporate references to how functions under study might be useful in the real world, as I tutor (i.e. for dynamics, heat flow, stress/strain calculations, etc.).

### Chemistry

I can offer help ranging from the basics (atomic and molecular bonding and structures, reaction and property trends on the periodic table, reaction stoichiometry and energetics, and equilibria) to practical applications, based on my ~20 years as an analytical chemist, in both pharmaceutical (generic and ethical) and chemical engineering workplaces, and four years of teaching various sciences at various academic levels.

### Geometry

Geometry courses vary widely in their pacing and rigor. Whether you have a standard curriculum geared towards learning theorems and applying them sequentially in proofs, or a higher-level one aimed at making you rigorously derive all theorems from a small set of definitions, I can work with you to motivate the material.

### Organic Chemistry

Organic chemistry - the study of carbon-containing compounds - is a broad field which connects smoothly to many others. I can help you understand structure and bonding in molecules, retrosynthetic analysis of molecules and their synthesis from "readily available starting materials", reactions of both simple moieties (driven by local configuration and having simple transition states) and larger assemblages (with stereochemistry and conformations), pericyclic and photochemistry, reaction dynamics, and use of other intermediates - carbenes, carbanions, and radicals - to accomplish multistep syntheses. My background includes ~20 years professionally working as an analytical chemist in pharmaceutical and chemical engineering industries (solving separation and synthesis challenges), four years of teaching various sciences at various academic levels, and tutoring.

### Physical Science

I can offer help in this academic area, based on considerable use of its concepts during ~20 years of working as an analytical chemist in pharmaceutical and chemical engineering workplaces, and teaching physical science at the high school level.

### Physics

I can offer help on all aspects of physics, based on thorough knowledge from undergraduate studies, and applying its principles throughout an approximately 20 year career as an analytical chemist in pharmaceutical and chemical engineering workplaces. Basically, physics requires thinking in precise detail about the interactions of matter and energy in specific situations, and reducing these thoughts to appropriate mathematical expressions. (There are a few essential "arbitrary" rules to learn, also, but not very many!)

### Precalculus

Precalculus is a catch-all designation for math courses that relate algebra, geometry, and trigonometry together. Students become familiar with manipulating pieces of algebraic expressions, with assigning equations to given triangles, and with recognizing forms of equations, all of which they will use as they move into calculus later.

Thinking analytically in this way about real-world problems is the foundational skill necessary to solving them; this is what I teach as I tutor.

### SAT Math

SAT math includes general concepts of numbers, precedence of operations, functions used in algebra (see my specific listing on that), geometry and measurement (using similar triangles to solve real-world problems), reduction of data to analyse it, statistics (mean, median, mode, and standard deviation and variance), and probability operations (figuring numbers of permutations and combinations and using outcomes correctly in calculations).