Georgia Tech Tutoring
I have frequently tutored students at Georgia Tech, and am now particularly familiar with its curriculum in a few of its courses.
I’m especially familiar with the content of its Distance Math program, offering
Linear Algebra (1554)
Multivariable Calculus (2551)
Combinatorics (3012)
Differential Equations (2552)
I have also tutored regular Georgia Tech students (i.e. not enrolled through the Distance Math program). I am familiar with the content of their courses in
Linear Algebra
Differential Equations
Differential and Integral Calculus
Mathematical Statistics
Summer Prep
Each summer I offer a low-price course designed to prepare students who will take Georgia Tech Distance Math courses next semester. In this course we cover the fundamentals of linear algebra for year 1 students, and combinatorics for year 2 students.
Please contact me if you’re interested in this summer course—I only hold these courses if there are at least three students interested in attending for the entire summer program.
Logistics
Meetings are held in groups of at most 5 students, once a week for one hour. There are nine meetings in total
The location is TBD, I’ll take a survey of everyone interested and try to find a common convenient location.
Exact dates and times are TBD, but usually start in June and end by August.
Price
$30 per student per hour.
Structure
For the most part, I don’t teach! I answer questions!
On the first day I’ll give a one-hour introductory lecture. After that I’ll send students assigned exercises and reading. The reading should not take more than 2 hours, and the exercises should not take more than 2 hours.
After the first meeting, every week I will hold a one-hour in-person meeting, during which students can ask questions. The entire hour is driven by student questions, which can be anything related to our subject—I don’t prepare any lecture.
And at that point we, will be in a consistent weekly rhythm: Assign exercises and reading, hold a discussion session, submit solutions. Repeat week after week for 9 weeks, with a one-week break in the middle.
Policies
This course is designed to be slow-paced, and low-pressure. I want to leave students with a lot of time over the summer to have fun!
However, this course requires all students in the class to be on the same page and progress together. So students should expect to put in two hours of study per week, and if they fall behind then they may not be able to continue with the course.
All meetings start and end exactly on schedule--feel free to arrive a few minutes early, but if you're late then you just miss the class.
Linear Algebra
For students preparing to take linear algebra, we will cover the following topics:
Week 1: Systems of equations, geometry, and row-reduction.
Week 2: The dot-product, matrix product, and matrix equations.
Week 3: Vector equations, independence, span.
Week 4: Vector subspaces and bases.
Week 5: Linear transformations.
Week 6: Transpose, column space, row space, null space, range, and rank-nullity.
Week 7: Matrix inverse and determinant.
Week 8: Eigenvectors, eigenvalues.
Week 9: Diagonalization.
For lack of time, we won't be able to cover: Leonteif models, LU factorization, block matrices, homogeneous coordinates, complex eigenvalues, Markov chains, orthogonality, least-squares, Gram-Schmidt process, QR decomposition, constrained optimization, and SVD.
Applied Combinatorics
Week 1: Sets, lists, intersection, union, complement, difference, subsets, and the power set.
Week 2: Set products, relations, and functions.
Week 3: Cardinality, counting, union counting.
Week 4: The fundamental counting principle, permutations.
Week 5: Combinations, double-counting, and multinomials.
Week 6: Combinatorial proof.
Week 7: Stars-and-bars, solving constrained linear integer equations.
Week 8: PIE, exactly, at most, counting surjections, derangements
Week 9: Generating functions