Hemanshu Kaul: Curriculum Development and Teaching

Home Research Papers Teaching Mentorship Miscellany

Multivariate and Vector Calculus (Math 251): Spring 2012, Spring 2011, Fall 2007.

Elementary Linear Algebra (Math 332): Fall 2024, Fall 2022, Fall 2019, Fall 2017, Fall 2011, Fall 2009, Fall 2008, Fall 2006.

Introduction to Math Modeling (Math 380): Spring 2023, Spring 2022, Spring 2021, Spring 2019, Spring 2018, Spring 2017, Spring 2016.

Linear Optimization (Math 435): Spring 2024, Spring 2022, Spring 2020, Spring 2018, Spring 2016, Spring 2014, Spring 2012, Spring 2010, Spring 2008.

Introduction to Graph Theory and applications (Math 454): Spring 2024, Spring 2020, Fall 2014, Fall 2012, Fall 2010, Fall 2007.

Optimization I (Math 535): Spring 2024, Spring 2022, Spring 2020, Spring 2018, Spring 2016, Spring 2014, Spring 2012, Spring 2010, Spring 2008.

Discrete Applied Math I/ Graph Theory (Math 553): Fall 2018, Fall 2017, Fall 2016, Fall 2015, Fall 2014, Fall 2012, Fall 2010, Fall 2007.

Modern Methods in Discrete Applied Math (Math 554): Spring 2023, Spring 2021, Spring 2019, Spring 2017, Spring 2015, Spring 2013, Spring 2011, Spring 2009.

Teaching Experience at UIUC.
Independent Instructor for: Introductory Linear Algebra; Calculus and Analytic Geometry II.
Teaching Assistant for: Linear programming; Graph Theory; Introduction to Combinatorics; Combinatorial Mathematics.

Computational Decision Science and Operations Research (CDSOR), a new inter-disciplinary graduate program in College of Science developed in 2014-15 (with Sanjiv Kapoor, CS), approved in summer 2015, and new students admitted from Spring 2016.

I helped develop (as chair of the committee in 2018-19) a modernized and completely restructured M.Sc. program in Applied Math with remarkable flexibility for students to pursue a curriculum that can range from a traditional M.Sc. with thesis to a modern M.Sc. with a choice of specialization in a wide variety of contemporary applied fields in Mathematics, that was approved in 2019, with new students admitted from the same year.

Math 332: Elementary Linear Algebra: Revised the existing course to better suit students from Applied Math, CS, and Engineering by creating an exciting mix of rigorous proofs, algorithms, and applications. Syllabus; Discussion and Course.

Math 380; Math 486/522: Mathematical Modeling: developed new course to build understanding of applied mathematics as a thought-process and a toolbox for the study of real-world phenomenon with an emphasis on the modeling process using concepts and tools from continuous, discrete, and probabilistic mathematics. A semester-long project on open-ended real-world problems that utilize their comprehensive mathematical knowledge to formulate, modify, justify, and computationally analyze models. Math 380 is now a required course for Applied Math majors and also attracts students from CS and other majors. Syllabus; Discussion and Course.

Math 400: Real Analysis: developed new flipped version of the course with pre-recorded video lectures, lecture notes, weekly problems for in-class discussion, HW problems with content related to extracurricular historical and analytic content as well as connections with other parts of mathematics. This course transformation was very well received by the students, despite online teaching during the pandemic. All material available at Course.

Math 410: Number Theory: developed new course on fundamentals of number theory and its modern applications in cryptography, which has attracted undergraduate students from Applied Math, CS, and ECE Syllabus; Discussion and Course.

Math 435: Linear Optimization: developed new course incorporating the geometric and linear algebraic basis of algorithms, duality, integer programming, and applications to large scale optimization, which has attracted graduate and undergraduate students from Applied Math, CS, Physics, ECE, Chem. Engg., Data Science, CDSOR Syllabus; Discussion and Course.

Math 454: Introduction to Graph Theory and Applications: Revised existing joint undergrad-grad course to make it an appropriate course for undergraduate students from various backgrounds with an emphasis on building a strong foundation in discovering and communicating discrete mathematics. It attracts students from Applied Math, CS, ECE, and Physics. Course.

Math 535: Linear Optimization: Developed new course incorporating the geometric and linear algebraic basis of algorithms, duality, integer programming, and applications to large scale optimization, which has attracted graduate and undergraduate students from Applied Math, CS, Physics, ECE, Chem. Engg., Data Science, CDSOR. Syllabus; Discussion and Course.

Math 553: Discrete Applied Math I (Graduate Graph Theory): Replaced existing joint undergrad-grad course with a core-course for graduate students with advanced topics that incorporate modern probabilistic and algebraic techniques. It has attracted students from Applied Math, CS, Physics, and ECE. Course.

Math 554: Discrete Applied Math II (Modern Methods in Combinatorics): developed new course in Combinatorics applying modern methods from probability, multivariate polynomials, linear algebra, entropy, MCMC, etc. that has attracted graduate and talented undergraduate students from Applied Math, CS, and ECE. Syllabus and discussion; Course.

Topics in Probabilistic Methods for Discrete Mathematics: Proposal and Course. THe course attracted faculty and students from Math, CS, Physics, and ECE.

Discrete and Convex Geometry : Proposal. This proposal was approved and was taught by a faculty member in 2003.

Board of Trustees Award for Excellence in Teaching 2019, University-wide award, IIT.

Invited to propose, develop, and teach, a new graduate course in advanced combinatorics, Department of Mathematics, University of Illinois at Urbana-Champaign, Fall 2005.