1st lesson free
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Sebastian
- Rate US$28
- Response 1h
-
Students1
Number of students Sebastian has accompanied since arriving at Superprof
Number of students Sebastian has accompanied since arriving at Superprof
US$28/hr
Contact
1st lesson free
- Mathematics
- Algebra
- Logic
- Algorithms
- Pre-calculation
Pure and applied mathematician. Former professor at UCSD (US) and at UNAM (Mexico).
- Mathematics
- Algebra
- Logic
- Algorithms
- Pre-calculation
Lesson location
About Sebastian
I have a strong foundation in Pure Mathematics, which has equipped me with skills in abstract reasoning and mathematical formalism. For my bachelor's thesis, I summarized key results in rings, fields, and Galois Theory. Later, during my master's research, I explored algebraic structures further, focusing on Abelian groups that do not arise as the additive structure of a ring. My PhD studies at Universidad Nacional Autónoma de México (UNAM) expanded into Category Theory, Lattice Theory, and Module Theory, where I made my first original contributions to these areas. Beyond pure mathematics, my research has evolved to include applied mathematics, particularly in neuroscience and computer science. During my postdoctoral appointment at the University of California, San Diego, I applied Category Theory to bioengineering and neuroscience. One of my projects involved using categorical techniques to establish a connection between directed and undirected graphs while preserving directional properties, enabling the application of undirected graph methods to directed settings. In addition to applied research, I have also explored theoretical and philosophical aspects of mathematics. Specifically, I developed a formal framework suggesting that information flows through paths of least resistance. This work involved generalizing the notion of persistence in quiver representations using preradicals and applying it to model information flow in neural networks. By incorporating universal constructions such as limits and colimits, I provided a rigorous mathematical foundation for this concept.
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About the lesson
- Compulsory School
- Secondary School
- Higher Education
- +5
levels :
Compulsory School
Secondary School
Higher Education
Adult Education
Master
Doctorate
MBA
Pre-School
- English
All languages in which the lesson is available :
English
I began my teaching journey as a teaching assistant during my final years as an undergraduate student at Universidad Nacional Autónoma de México (UNAM) in Mexico City. In this role, I mentored students in Basic Algebra, Linear Algebra, and Complex Analysis. I quickly developed a deep appreciation for one-on-one interactions, as they allowed me to listen to students’ questions, understand their struggles, and identify why certain concepts were confusing. I realized that transitioning to university-level mathematics requires a significant shift in thinking, as the skills needed differ greatly from those developed in high school. By guiding students through verbalizing their reasoning, I helped them recognize common mathematical misconceptions and gain a clearer understanding of the rigor that mathematical thinking demands.
During my master's studies, I became a lecturer at UNAM, where I taught courses such as Basic Algebra I & II (covering set theory, natural numbers, induction, integer construction, divisibility, and polynomial rings), Linear Algebra I & II (including vector spaces, linear transformations, determinants, diagonalization, and Jordan canonical forms), and Abstract Algebra I (focusing on the theory of finite groups).
Afterward, I continued teaching as a lecturer in the Mathematics Department at the University of California, San Diego (UCSD) immediately following my postdoctoral appointment in the Department of Bioengineering at UCSD. In my first academic year, I taught a range of courses, including Math 18 (Linear Algebra), Math 109 (Mathematical Reasoning), Math 10C (Vector Calculus), and Math 3C (Precalculus).
Throughout my teaching career, I have emphasized the importance of fostering an interactive and supportive learning environment. I incorporate opportunities for students to ask questions and engage with the material in a way that makes mathematical thinking more accessible. I believe that mathematics is a valuable skill for any profession, and my teaching philosophy revolves around creating classrooms where students can develop strong reasoning skills. By centering instruction around questions and misconceptions, I tailor my approach to accommodate different levels of interest and knowledge, ensuring that students who put in the effort have the support they need to succeed.
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Rates
Rate
- US$28
Pack prices
- 5h: US$140
- 10h: US$280
online
- US$28/h
free lessons
The first free lesson with Sebastian will allow you to get to know each other and clearly specify your needs for your next lessons.
- 1hr
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