Jason Qin has been busy with Linear Algebra with Applications classes at Yale University, while juggling his time between finals at IMSA and the American Regions Math League at Iowa. He is excited to report on his experiences at Yale.
“This first week, I learned a lot about the basics of linear algebra (vectors, matrices, systems of linear equations) and the instructor really tried to build up a solid geometrical understanding of our knowledge in the topic, which I found really rewarding. I had always known about the formula or algebraic method to perform certain math topics, like multiplying matrices together, but I never had a solid understanding of “why?” until this course, which I greatly appreciate,” Jason reports.
“The overall structure of the course is a one and half hour zoom meeting Monday to Friday and an associated quiz on Friday over the topics we covered that week. There would also be homework after every class to be submitted using Canvas. The instructor encouraged a collaborative approach to learning and finishing homework assignments and I am able to contact and connect with my fellow peers using GroupMe, which I find extremely helpful,” Jason adds.
“The second week of the Yale Summer Program for Linear Algebra is going pretty well! We learned a lot more about the essence of the course: vectors, transformations, and matrices. I found transformations to be super cool, especially thinking of matrices as just a mathematical representation of geometric linear transformations instead of pure mathematical constructs. Like last week, the instructor made sure to keep a geometric perspective to encourage greater understanding into why a certain topic works instead of just a formula. For example, I always knew of a formula to find inverse matrices, but the course greatly facilitated my understanding of why this certain formula works and what exactly the inverse even means on a tangible level,” Jason explains.
“Also, more about the layout of the course; the homework is to be turned in on a program called Gradescope, where the Teaching Assistant can easily grade and give feedback for each specific problem,” Jason adds.
“Throughout these five weeks, I learned a lot about the basics of linear algebra, specifically with a focus on its applications. I also really loved the focus of the course on understanding the concepts and not just learning how a technique worked. I have always been curious about the STEM fields and mathematics, so I really enjoyed all the answers to the “why?” question for all the math concepts in this course. The course synthesized and strengthened my fundamental knowledge of linear algebra topics that I had already known of, such as dot products or matrix multiplication, and new topics that are extremely important towards the real world and associated applications of the course, such as eigenvalues and eigenvectors. In addition, the instructor made sure to emphasize understanding with the geometric background and understanding for everything that we learned. For example, I had known about the determinant of a matrix and how to calculate it using techniques and formulas, but I didn’t know what exactly it represented in terms of linear transformations and scaling factors. However, after developing a strong understanding of the basics of linear algebra, especially matrices, in a geometric lens, the course presented the idea of the determinant of a matrix in a clear and geometrically backed up way,” Jason reports.
Jason is appreciative of the opportunity to study mathematics in greater depth this summer as a result of the GFF sponsorship.
“Overall, thanks to the Garwin Family Foundation, I was able to continue pursuing my passion in mathematics and its applications this summer. I am extremely grateful for the sponsorship from the program to allow aspiring students like myself to pursue their passions. I really learned a lot in the topics of linear algebra and loved the exploration of its applications. The course provided me with a strong foundation on a cornerstone topic in mathematics, and I feel more than prepared to explore higher level math concepts and their applications in the future,” Jason exclaims!
Great work, Jason! We wish you much success in pursuing your passion for mathematics.
>> Read Jason Qin’s final report (PDF file, 40 KB).
>> Learn about other students’ experiences in the GFF Scholarship Program.
