Zhiguo Yang
Applied and Computational Mathematics · Shanghai Jiao Tong University
Teaching

Teaching and Mentoring

My teaching emphasizes learning by doing, conceptual clarity, and intellectual independence. I want students to connect rigorous mathematics with meaningful problems and to grow into active, self-directed learners.

Teaching Profile
  • 12 course offerings since September 2020.
  • 43 credits and approximately 688 teaching hours.
  • Courses at both undergraduate and graduate levels in computational and applied mathematics.

Teaching Philosophy

I believe teaching should do more than convey knowledge. It should help students learn how to learn, think clearly, connect theory with applications, and develop the judgment to decide what is worth solving and how to solve it well.

In both teaching and supervision, I emphasize problem-driven learning, first-principles explanation, and active engagement with genuine questions from science, engineering, optimization, computation, and increasingly AI-related contexts.

Teaching Awards
  • University-Level Outstanding Class Advisor Award, Shanghai Jiao Tong University (2025).
  • Excellence Award, Fifth Young Faculty Teaching Competition, Shanghai Jiao Tong University (2021).
  • Second Place, Young Faculty Teaching Competition, School of Mathematical Sciences, Shanghai Jiao Tong University (2021).

Courses Taught

Graduate Courses
  • Advanced Computational Methods
  • Optimization Methods
  • Numerical Methods for Differential Equations
Undergraduate Courses
  • Numerical Methods
  • Linear Algebra

Student Mentoring and Research Training

I view advising as an extension of teaching. My aim is not only to help students complete projects, but also to help them formulate questions, read papers efficiently, write clearly, present their work effectively, and build confidence as independent researchers.

  • Supervised undergraduate theses, master's graduates, Ph.D. graduates, and postdoctoral researchers.
  • Current and former mentees have gone on to positions at the Chinese Academy of Sciences, Nanyang Technological University, and Jiangsu Normal University.
  • Student work has led to publications in venues including SIAM Journal on Scientific Computing , Nature Communications , Journal of Computational Physics , and Journal of Scientific Computing .
Recent Supervision Snapshot
Ph.D.
Lechang Qin and Zixuan Gao graduated in 2025; current Ph.D. students include Yuanxiang Huang, Yun Wu, Taoqi Ren, Hanbin Wang, and Zijing Zhu.
Postdoc
Sen Lin (2023–2025), later Assistant Professor at Jiangsu Normal University.
Advising
Also served as class advisor for the 2021 “Qiangji” class throughout the students’ four-year undergraduate cycle.

Representative Student Feedback

“This is the best mathematics course I have taken at SJTU.”
“The instructor explains not only the results, but also the underlying principles and motivations.”
“The instructor is able to connect optimization theory with practical engineering applications.”

Teaching Approach in Practice

  • Problem-first course design built around motivating examples.
  • Teaching from first principles while keeping real applications in view.
  • Adaptive course refinement based on student feedback and background.
  • Project-based learning and open-ended assignments.
  • Research apprenticeship as a route to independence.