Mechanics forms the basic background for the understanding of physics. This course on Classical, or Newtonian mechanics, considers the interactions which influence motion. These interactions are described in terms of the concepts of force, momentum and energy. Initially the focus is on the mechanics of a single particle, considering its motion in a particular frame of reference, and transformations between reference frames. Then the dynamics of systems of particles is examined.

The first half of the semester will give an introduction to the basic ideas of classical oscillations and waves. Topics include simple harmonic motion, forced and damped harmonic motion, coupled oscillations, normal modes, the wave equation, travelling waves and reflection and transmission at interfaces. The second half of the semester will first give an introduction to Einstein's special relativity, including evidence for the frame-independence of the speed of light, time dilation, length contraction, causality, and the relativistic connection between energy and momentum. Then we will follow the historical development of quantum mechanics with the photo-electric and Compton effects, the Bohr atom, wave-particle duality, leading to Schrödinger's equation and wave functions with a discussion of their general properties and probabilistic interpretation.

The first half of the semester will continue with the development of quantum mechanics. Topics will include Shrödinger's wave mechanics, tunneling, bound states in potential wells, the quantum oscillator, and atomic spectra. The second half of the semester will give an introduction to the basic ideas of classical statistical mechanics and radiation, with applications to experimental physics. Topics will include Boltzmann's interpretation of entropy, Maxwell-Boltzman statistics, energy equipartition, the perfect gas laws, and blackbody radiation.

Experiments in this course are designed to form a bridge to current experimental research. A wide range of experiments are available using contemporary techniques and equipment. In addition to the standard set of experiments a limited number of research projects are also available. Many of the experiments can be carried out with a focus on instrumentation.

Experiments in this course are designed to form a bridge to current experimental research. A wide range of experiments are available using contemporary techniques and equipment. In addition to the standard set of experiments, a limited number of research projects may be available. This laboratory is a continuation of PHY327H1.

The course is intended to provide an introduction and a very interdisciplinary experience to robotics. The structure of the course is modular and reflects the perception-control-action paradigm of robotics. The course, however, aims for breadth, covering an introduction to the key aspects of general robotic systems, rather than depth, which is available in later more advanced courses. Applications addressed include robotics in space, autonomous terrestrial exploration, biomedical applications such as surgery and assistive robots, and personal robotics. The course culminates in a hardware project centered on robot integration.

The course addresses advanced mathematical concepts particularly relevant for robotics. The mathematical tools covered in this course are fundamental for understanding, analyzing, and designing robotics algorithms that solve tasks such as robot path planning, robot vision, robot control and robot learning. Topics include complex analysis, optimization techniques, signals and filtering, advanced probability theory, and numerical methods. Concepts will be studied in a mathematically rigorous way but will be motivated with robotics examples throughout the course.

An introduction to the fundamental principles of artificial intelligence from a mathematical perspective. The course will trace the historical development of AI and describe key results in the field. Topics include the philosophy of AI, search methods in problem solving, knowledge representation and reasoning, logic, planning, and learning paradigms. A portion of the course will focus on ethical AI, embodied AI, and on the quest for artificial general intelligence.

This course will introduce students to the topic of machine learning, which is key to the design of intelligent systems and gaining actionable insights from datasets that arise in computational science and engineering. The course will cover the theoretical foundations of this topic as well as computational aspects of algorithms for unsupervised and supervised learning. The topics to be covered include: The learning problem, clustering and k-means, principal component analysis, linear regression and classification, generalized linear models, bias-variance tradeoff, regularization methods, maximum likelihood estimation, kernel methods, the representer theorem, radial basis functions, support vector machines for regression and classification, an introduction to the theory of generalization, feedforward neural networks, stochastic gradient descent, ensemble learning, model selection and validation.

The Robotics Capstone Design course is structured to provide students with an opportunity to integrate and apply the technical knowledge gained throughout their degree program toward the solution of a challenging real-world robotics problem. During the half-year course, students work in small teams and have considerable freedom to explore the design space while developing a complete robotic hardware and software system. The challenge task incorporates all aspects of the "sense-plan-act" robot design paradigm, with designs assessed based on engineering quality and performance relative to a series of benchmarks. In addition, each student completes a critical reflection on their team's performance and the evolution of their experience with design during their undergraduate program. Students are supported by a teaching team comprised of domain experts.

An introduction to aspects of computer vision specifically relevant to robotics applications. Topics include the geometry of image formation, image processing operations, camera models and calibration methods, image feature detection and matching, stereo vision, structure from motion and 3D reconstruction. Discussion of the growing role of machine learning and deep neural networks in robotic vision, for tasks such as segmentation, object detection, and tracking. The course includes case studies of several successful robotic vision systems.

The course addresses fundamentals of mobile robotics and sensor-based perception for applications such as space exploration, search and rescue, mining, self-driving cars, unmanned aerial vehicles, autonomous underwater vehicles, etc. Topics include sensors and their principles, state estimation, computer vision, control architectures, localization, mapping, planning, path tracking, and software frameworks. Laboratories will be conducted using both simulations and hardware kits.

Describes important fixed income securities and markets. The course emphasizes traditional bond and term structure concepts crucial to understand the securities traded in these markets. Students are required to work in the Rotman Financial Research & Trading Lab to solve the assigned problems using real time data. Not eligible for CR/NCR option. Contact Rotman Commerce for details.

This course examines the ways in which risks are quantified and managed by financial institutions. The principal risks considered include market risk, credit risk and operational risk. The course also covers the evolution of bank regulation and the regulatory limits on risk taking. Not eligible for CR/NCR option. Contact Rotman Commerce for details.

This course will use finance theory applied with Excel applications to understand potential returns and risks inherent in particular investment/trading strategies. Learning-by-doing will be facilitated by simulation-based Rotman Interactive Trader cases focused on particular risks. This training will be analogous to using a flight simulator for learning to fly. Not eligible for CR/NCR option. Contact Rotman Commerce for details.

Introduction to data analysis with a focus on regression. Initial Examination of data. Correlation. Simple and multiple regression models using least squares. Inference for regression parameters, confidence and prediction intervals. Diagnostics and remedial measures. Interactions and dummy variables. Variable selection. Least squares estimation and inference for non-linear regression.

An overview of probability from a non-measure theoretic point of view. Random variables/vectors; independence, conditional expectation/probability and consequences. Various types of convergence leading to proofs of the major theorems in basic probability. An introduction to simple stochastic processes such as Poisson and branching processes.

Programming in an interactive statistical environment. Generating random variates and evaluating statistical methods by simulation. Algorithms for linear models, maximum likelihood estimation, and Bayesian inference. Statistical algorithms such as the Kalman filter and the EM algorithm. Graphical display of data.

Discrete and continuous time processes with an emphasis on Markov, Gaussian and renewal processes. Martingales and further limit theorems. A variety of applications taken from some of the following areas are discussed in the context of stochastic modeling: Information Theory, Quantum Mechanics, Statistical Analyses of Stochastic Processes, Population Growth Models, Reliability, Queuing Models, Stochastic Calculus, Simulation (Monte Carlo Methods).

Complementary Studies elective

Entrepreneurship is the practice of identifying, creating, and capturing value – whether by launching a new venture or driving innovation within an existing organization. Engineering students will be introduced to the entrepreneurial mindset and toolkit through a structured, practical, and experience-based approach. Students will explore every stage of the entrepreneurial journey, from identifying unmet needs and designing value propositions to building business models, pitching ideas, and understanding the real-world mechanics of marketing, sales, finance, and leadership.

Topics include:
• Value creation, strategic thinking, and positioning
• Market research, innovation, and business model design
• The 4Ps of marketing, segmentation, targeting, and branding
• Organizational behavior, teamwork, and leadership
• Accounting, finance, and legal for early-stage ventures
• Sales, persuasion, and behavioral decision-making
• Pitching, scaling, and storytelling

Guest lectures from real entrepreneurs will be brought in and the work will be grounded in real-world cases and hands-on projects. No prior business experience is required.

This is the first of two complementary entrepreneurship courses (followed by TEP432) designed to help engineering students apply their problem-solving skills to the creation of ventures, products, and ideas that matter.

Humanities and Social Science elective

An examination of representations of science/scientists in theatre. Reading and/or viewing of works by contemporary playwrights and related materials on science and culture. Critical essays; in-class discussion and scene study.

Humanities and Social Science elective

Introduces students to the history, theory and practice of communicating science to the public. We first establish a theoretical foundation for understanding the complex relationship between science, scientists, and the public, closely examining techniques and strategies for communicating about science to non-technical readers with a variety of backgrounds and ideological perspectives. We apply these concepts to contemporary case studies in multiple media, focusing on (mis)representations of climate, environmental, and biomedical sciences, breakthroughs in engineering. In doing so, we explore how the shift from traditional news to new media – including videos, podcasts, and social media – has changed how science is communicated to the public, plus the implications of this shift for scientists and engineers.

Humanities and Social Science elective

This course explores Rhetoric historically to understand its development and practically to understand how ideas are constructed, disseminated, shared or imposed. The course explores worldview - the organizing structure by which we view the world - to position the student as rhetorically effective in multiple contexts. Students analyze political, cultural, and scientific discourse from great speeches to advertising to research papers. Students develop their rhetorical, communication, and persuasive abilities.

The purpose of this course is to enable future engineers to initiate, facilitate and moderate discussion between stakeholders with differing and/or opposing values and ideologies. The relationship between engineering and the concepts of social justice to develop the skills needed to take practical action in a complex world is explored. This course facilitates building personal responses to ideas of justice, bias and marginalization. These ideas affect Engineers and Engineering in general, domestically and globally, in projects and in contexts, such as the workplace and academic environment. Readings will be drawn from current writers on Engineering and Social Justice. Students will rehearse action through theatre techniques, developed to enable communities to practice and critique action.

In this course, students will explore the creative writing process, with an emphasis on the giving and receiving of critical feedback. This exploration will reinforce the iterative principles of the engineering design process and will provide students with flexible and transferable tools for them to apply to future engineering work. They will examine up to two genres of creative writing (fiction, science fiction, poetry, creative non-fiction, screenwriting, playwriting, etc.) in order to hone their own creative and critical thinking skills. Students will be introduced to relevant elements of craft, will analyze representative literary examples, will create original creative work both in generative weekly exercises and in longer at-home assignments, will give and receive feedback from their peers through structured in-class workshops, and will apply this feedback to their own writing.

Upon graduating university and entering the workforce, engineering students have little idea about how frequently in their professional lives their interactions, decisions, and actions will touch on various areas of law. This course is designed to highlight the amount of overlap between these two pillars in today's society. Some examples include: acting as an expert witness, preparing a patent, creating a contract for supplies and more. By the end of this course, students will have a working understanding of the intersection between Engineering and Law, and be able to navigate the legal complexities in their professional and business lives.

Focusing on the overlaps between engineering and science fiction, it is important to consider the multiple crossovers between these two fields of study: both contain a sustained focus on technology and its application to real-world problems; both consider the impact of new technologies on humans, animals, and the surrounding environment; and, perhaps most importantly, both imagine future worlds in order to build infrastructures, social structures, industry, and cultural practices capable of addressing current and future technological, political, social, and environmental crises.

The curriculum will showcase how creative writing connects to, and enhances, critical thinking in engineering. We will cover major concepts in science fiction (e.g., biomedical breakthroughs, artificial intelligence, terraforming planets) to study the ways its stories have explored, questioned, predicted, and even inspired elements from various engineering disciplines. We will seek to gain an understanding of how science fiction allows us to reflect on engineering practice and ethics, projecting the societal and environmental impacts of untested technologies. We will develop critical reading and academic writing skills to explain the importance of imagining what we intend to build as a prerequisite to building.

Complementary Studies elective

Develop a practical approach to being a more productive engineer, based on the premise that for technology to become a reality, it must be translated through people. A key is understanding engineers lead in ways that reflect their skills and mind set. Learning frameworks and personal working styles inventories provide practical tools to assist the student to understand human nature and to become a competent leader of self and of teams. The student prepares to become a competent leader by first developing a deeper understanding of self and then undertaking to learn (understand and integrate) key skills, character attributes,and purposeful behaviours. Strategies for development of high-performance teams are also presented. The material is delivered through lectures, readings, in-class discussion and a team project. Attendance is mandatory to enable learning through experiential activities and critical reflection.The project is based on the team interviewing a senior leader at an engineering-intensive company or senior leader in the community

Complementary Studies elective

The second of two complementary entrepreneurship courses builds on foundational training, diving deeper into the strategic, operational, and human complexities of entrepreneurship and venture creation. Students will engage with advanced tools and contemporary readings to explore how ventures grow, adapt, and respond to uncertainty in dynamic markets.

Key topics include:
• Growth strategy and scaling
• Competitive advantage and business model innovation
• Systems thinking and operations in scaling ventures
• Founder decision-making and psychological resilience
• Advanced leadership and managing through ambiguity
• Ethical dilemmas, failure, and learning loops
• Modern venture financing and cap table dynamics
• The intersection of technology and entrepreneurship

Students will work in teams to develop a venture concept in greater depth, integrating strategy, operations, financials, and go-to-market thinking into a coherent plan or prototype. Sessions will incorporate real-world case studies, founder guest speakers, and interactive discussions grounded in current research and practitioner insights.

Designed for students who want to deepen their entrepreneurial thinking, whether as future founders, innovators, or team leaders in fast-moving organizations.

We live in a data driven world, with the total volume of global data projected to be 181 zettabytes by 2025. New ways of measuring and analyzing data in the field of global development are opening the door to a better understanding of global challenges and data-driven innovations have significant economic and societal potential. For example in the healthcare sector, the use of new devices and analytics can improve diagnosis and triage of disease, improve health system efficiency, and reduce costs. However, there have also been many instances of sensing technologies and algorithms that perpetuate or enhance inequalities rather than reducing them. Through the use of lectures, case studies, readings, and guest speakers working at the health-water-climate nexus of global challenges, students will learn about innovations in sensing, and data analytics that are helping to advance the UN Sustainable Development Goals. They will learn to analyze and assess historical data and data that is currently being collected in the global development and engineering space and will critically examine examples of biases and flaws with the ways we develop sensors/measurements and train algorithms. Students will have a practical opportunity to develop entrepreneurship skills through proposing and researching a sensing or data analytics innovation for tackling global challenges, developing a business case for this innovation, and pitching their solution to their peers.