All of
Travis’s current tutoring subjects are listed at the left. You
can read more about
Travis’s qualifications in specific subjects below.
C++
I have completed two college level courses on computer programming in the C/C++ language. I received high A's on all exams in both classes and high A's for both course averages. I have a strong understanding of the important basic programming concepts, such as arrays, for-loops, while-loops, if/else statements, pointers, and string manipulation. I'm very comfortable writing complex programs for various applications, including sorting data, searching data, solving differential equations numerically, and solving problems requiring the generation of random variables. In addition, I have taken courses for programming with multiple other languages, including Matlab, Maple, SPSS, SAS, and R, all of which bear strong resemblance to the C/C++ language.
Computer Programming
I have completed two college level courses in C/C++ programming through the biomedical engineering program at the University of Alabama at Birmingham. The first class, Engineering Computation, offered a comprehensive overview of computer programming applications to solving engineering-based problems. The course focused on C/C++, because this language is considered a foundation for many other languages; a firm knowledge of C/C++ facilitates rapid acquisition of most of the fundamental programming languages. The major topics covered included variable declaration, array initialization, array organization, string manipulation, string concatenation, for-loops, while-loops, if-else statements, basic image design, and pointer indirection.
The course approached these topics from a standpoint of practical applications in engineering. One of the most important engineering applications in computer programming requires solving complex differential equations, which are often difficult (if not impossible) to solve theoretically or exactly. One example includes approximating the zeros of complex functions using Newton's Method, a technique covered extensively. Analysis of solving these equations also necessitates careful error estimation.
I made high A's on all three exams in the Engineering Computation course, including a perfect score on the first two exams. I also received a high A on the semester project, which required the creation of a 300-line program for sorting large arrays of data according to user-determined specifications and searching for specific elements within these arrays. I achieved high points on my project because of my program's efficient algorithm for sorting data without extensive memory depletion. I received an A for the final grade in the course.
Two years later, I completed a class called Biocomputation, an upper level biomedical engineering course emphasizing the application of computer programming toward specific problems in biomedical engineering. The course placed equal emphasis on Matlab and C/C++, which are considered two of the most salient and powerful programming languages. Because the course assumed a basic knowledge of fundamental programming concepts, most of the material focused on higher-level problem solving strategies. One of the most important applications included the solution of Laplace's differential equations as applied to fluid mechanics, specially when analyzing blood flow through capillaries. Much of the last half of the course focused on signal processing techniques, which are an important part of functional magnetic resonance imaging (fMRI) and bioimaging in general. I learned how to generate and augment random signals in order to form rudimentary three dimensional images.
The course on Biocomputation required three exams; I earned high A's on all exams. I achieved a perfect score on the second test and earned an A for the course.
Differential Equations
I earned an A in Introduction to Differential Equations at the University of Alabama at Birmingham, where I also received my math minor.
The course that I completed focused on the use of STELLA computer software in order to model and interpret physical problems involving differential equations. Topics that were covered in the course were homogenous and non-homogenous differential equations, separable equations, exact equations, Laplace transforms, and second-order equations. I scored A's on each of our quizzes, exams, and homework assignments.
Linear Algebra
I earned an A in Linear Algebra at the University of Alabama at Birmingham as part of my math minor. I can send a copy of my transcript in order to verify this information.
Some of the topics covered in the course were: solving multiple systems of linear equations, spaces and subspaces, span, matrices, determinants, fundamental theory of linear algebra, logical proofs, eigenvalues, and eigenvectors.
To go into a little more detail, the first part of the class consisted of solving systems of linear equations. Systems were solved first using Gaussian elimination.
Next, the course concentrated on the concept of vector spaces and subspaces, and how to prove whether or not a set of numbers was considered a vector space or subspace. Furthermore, basic rules of mathematical logic were introduced, such as negations, conditionals, deductions, and inductions.
The next part of the class focused on the nature of matrices and determinants--how to add matrices, subtract matrices, and multiply matrices. Students learned how to calculate determinants of square matrices. Students then learned an alternate way to solve systems of linear equations with the use of determinants--this is also known as Cramer's Rule.
The next part of the course was spent on defining the concept of span and whether or not two or more sets of vectors could be considered to span a vector space. It was proven that only vectors which are linearly independent may span a vector space. The vectors that can space a vector space form the basis of that space.
The last three weeks were devoted to the introduction of eigenvalues and eigenvectors. Students learned how to determine the eigenvalues of a matrix by using properties of determinants.
MATLAB
I have completed one college level course on computer programming with Matlab. I received high A's on all exams as well as a high overall A average for the course. I have a strong understanding of the important basic programming concepts, such as arrays, for-loops, while-loops, if/else statements, pointers, and string manipulation. I'm very comfortable writing complex programs for various applications, including sorting data, searching data, solving differential equations numerically, creating images, concatenating strings, and solving problems through the generation of random variables. In addition, I have taken courses for programming with multiple other languages, including C/C++, Maple, SPSS, SAS, and R, all of which bear strong resemblance to Matlab.