Teaching
2019/20 Fall/Winter
ISCI 1A24 and ISCI 2A18, the first and second year mathematics components in the Integrated Science (iSci) program at McMaster University.
The math portion of ISCI 1A24 is designed to develop a conceptual understanding of the fundamental principles of calculus and explore their relevance to other branches of natural sciences. The course covers standard topics in Calculus I & II: differential and integral calculus of functions of one variable, differential calculus of functions of several variables, sequences and infinite series; as well as polar coordinates and parametric curves, applications of calculus to probabilities and statistics, and an introduction to differential equations. Emphasis is placed both on the theoretical foundation and the practical integration of these mathematical concepts and principles with knowledge and skills from biology, chemistry, physics, earth science and psychology in the context of four major interdisciplinary research projects. ISCI 1A24 Outline.
The math portion of ISCI 2A18 extends integral calculus from the two dimensional world of single variable functions to higher dimensions; the main focus is understanding how the fundamental theorem of calculus generalizes to this new setting. The course covers multiple integrals, parametric curves and surfaces, line and surface integrals, conservative fields, and the integral theorems of Green, Stokes and Gauss. While the emphasis is placed on the geometric and physical interpretation of these concepts and results, other important applications of multivariable calculus to natural and social sciences are also discussed. As part of the integration with the other ISCI 2A18 components, the course touches on additional topics such as Fourier series, partial differential equations, and multivariate probabilities and statistics. ISCI 2A18 Outline.
2019 Fall
MATH 3MB3 - Introduction to Modelling
The course is designed to introduce the students to computational modelling using Python. The overall course goals include: to learn to apply mathematical tools to solve open-ended, real-world problems, as well as to understand the benefits and limitations of mathematical modelling and to critically assess the predictions based on mathematical models. The aim is to stimulate students' interest in studying more advanced topics such as numerical analysis, differential equations, probability and statistics, and optimization. The course will focus on modelling of complex systems and will cover deterministic (discrete-time and continuous-time) and stochastic models. The course includes a scientific communication component consisting of a group project. Students identify a research question related to a real-world situation, write a research proposal, and work in groups to build a computational model that generate additional perspectives and insight in tackling their question. The results are presented in the form of a written report and through an in-class presentation. Students engage in peer-review and feedback activities for the project written deliverables and oral presentations. MATH 3MB3 Outline.
2020 Winter
STATS 4A03/6A03 - Time Series
Time series analysis is concerned with data consisting of time-ordered sequences of measurements on some phenomenon of interest. These type of data are common in many areas, including business (weekly interest rates, daily closing stock prices), climate (daily high and low temperatures, annual amount of precipitation), agriculture (annual crop and livestock production figures, annual export sales), public consumption (hourly provincial hydro demand, yearly garbage amount produced by a city), and many others. Unlike most other statistical data, time series data show correlation over time, called autocorrelation. In addition, data often show trends such as linear, polynomial, seasonal and sinusoidal patterns. Using a systematic approach, we will learn how to extract information about the characteristics of phenomena that generates a time series, how to model the stochastic mechanism that gives rise to an observed time series, and how to forecast the future values of a series based on its history. The course includes a scientific communication component consisting of a group project. Students will use R to carry out time series model building and analysis of real-life data. The findings will be presented in the form of a written report and a poster presentation. Students will engage in peer-review and feedback activities for the project deliverables. STATS 4A03/6A03 Outline.
See Avenue to Learn for up-to-date information presented in class.