All of
Sahel’s current tutoring subjects are listed at the left. You
can read more about
Sahel’s qualifications in specific subjects below.
Algebra 1
Algebra is the foundation for all higher level mathematics courses. It is the study of a set of rules on how to manipulate mathematical expressions and solve them efficiently.
A list of the most common topics in introductory Algebra includes: Functions and Patterns, Linear Equations, Linear Inequalities, Polynomials, Factoring, Quadratic Functions, Exponential Functions, Radical Functions, Logarithmic Relations, Conic Sections, Sequences and Series, Probability and Statistics, Trigonometric Functions and Trigonometric Identities.
Algebra 2
Algebra is the foundation for all higher level mathematics courses. It is the study of a set of rules on how to manipulate mathematical expressions and solve them efficiently.
A list of the most common topics in introductory Algebra includes: Functions and Patterns, Linear Equations, Linear Inequalities, Polynomials, Factoring, Quadratic Functions, Exponential Functions, Radical Functions, Logarithmic Relations, Conic Sections, Sequences and Series, Probability and Statistics, Trigonometric Functions and Trigonometric Identities.
Differential Equations
Differential equations are mathematical statements relating the rate of change (or derivative) of a function to the function itself. Linear Algebra works great for modeling static situations, but more interesting phenomena in the real world include changing variables such as temperature, volume, population, etc. To understand these more interesting physical situations, one needs to find the differential equation describing the situation, be able to solve for the exact or approximate solution of it and also be able to interpret what that solution means.
I have taken two semesters of advanced mathematics courses in differential equations and boundary value problems as an undergraduate. More importantly, I have had years of practice with applications of differential equations. Many physics problems are modeled and solved using differential equations and as a physics major I am proficient in solving such problems.
Simplest mechanic and circuit problems such as damped or driven harmonic oscillator and LC or RLC circuits require knowledge of differential equations and how to solve them. As a physics teaching assistant and tutor, I have helped my students with mathematical background skills they needed (such as 1st, 2nd, and higher order homogeneous and non-homogeneous differential equations) to solve these problems.
Farsi
Persian or Farsi is the official language of Iran. Some other countries such as Tajikistan and Afghanistan which, at some point in history, were under the rule of Persian Empire also talk in Farsi (although there are slight differences as there are a few branches of Farsi language such as Pashto and Urdu).
I was born and raised in Iran and Farsi is my first language. I am fluent in both writing and speaking Farsi and have taken numerous Farsi grammar and Farsi literature classes back in Iran. From very early ages, I started reading legendary Persian poetry and history books such as "Divane Hafez" and "Shahname" to name only a few and this has helped me develop a much better understanding of the structure of this beautiful language. Not only am I fluent in speaking Farsi, I am also able to systematically teach it to others who also have found the beauty of it.
Linear Algebra
Linear Algebra is concerned with solving systems of algebraic linear equations. In introductory linear algebra, this is done using the technique of elimination which works for systems of two or three equations. However, when more than three equations need to be solved simultaneously, one needs to begin using arrays and matrices. Thus, central to linear algebra is the study of matrices and how to perform basic operation such as matrix multiplication. The notion of vector space and subspace becomes important and Eigenvalue problems will be introduced in more advanced linear algebra courses.
Quantum physics uses the language of linear algebra where wave functions and operators are described using abstract vectors and linear transformations respectively.
I have taken courses that thought linear algebra in high school and in university. I have also taken graduate level quantum courses which gave me advanced knowledge of the language of linear algebra.
As a teaching assistant and tutor in the subject of quantum mechanics for two semesters in UMN, I have helped my students with mathematical background skills they need in quantum physics such as working with N-dimensional vector space and calculating eigenvalues and eigenfunctions for various operators.
Physics
Physics is the study of our universe and how it works and it has many different branches.
Introductory physics courses will include Mechanics, Electromagnetism, Thermal Physics, Quantum Physics and Relativity.
A list of most common topics in mechanics include motion in two and three dimensional space, circular motion, force and torque, energy, power, Newton's laws, Kepler's laws, linear and angular momentum and their conservations and the gravitational force.
A list of most common topics in electromagnetism include Coulomb's law, Gauss's law, Biot-Savart law, Ampere's law, Lorentz force law, Faraday's law and Maxwell's equations.
A list of most common topics in thermal physics include the three thermodynamic laws, entropy and discussion of engines.