Author: orientation

Transportation Systems Engineering

Posted on by orientation

Q: Why is the transportation engineer always invited to parties?

A: They know how to keep things flowing.

What is Transportation Systems Engineering? 

Transportation Systems Engineering is EngSci’s newest major and is the first undergraduate program of its kind in North America. As cities continue to grow, ensuring the efficient movement of people and goods has become increasingly complex. Rising populations and greater demand for transportation require new solutions to improve mobility and reduce congestion. This major helps address the need for experts in this growing field. The program offers a unique combination of specialized focus, technological emphasis, interdisciplinary integration, and alignment with U of T’s research strengths. 

This major is a combination of two pillars of transportation engineering:  

  • Transportation planning and operations (informatics, traffic and road network modelling, and transportation economics)  
  • Emerging technologies (vehicle automation, big data/machine learning, and sustainability)

Students can expect to work on complex transportation design projects, such as transit priority corridors, complete streets and cycling networks, or automated vehicle systems, with guidance from industry leaders. 

[Source]

Why Choose This Major? 

If you’re interested in:  

  • Using informatics and big data to solve complex, real-life problems millions of people’s lives 

  • Working with emerging technologies such as autonomous vehicles  

  • Using travel and mobility modeling to inform infrastructure and transit development  

  • Integrating micromobility options (e-scooters, bikeshare, etc.) and autonomous trucks into transportation networks  

  • Using advanced technology to reduce gridlock and make urban transportation more sustainable  
  • Helping people and goods move efficiently  

  • Evaluating the economic impacts of transportation policies, projects, and investments 

then this major may be a great fit for you. 

Where Can This Major Where Can This Major Take You? 

Graduates of the Transportation Systems Engineering major have the skills needed to enter technology- and information-driven roles in transportation system planning, designing, and operation fields. They’re also well-equipped to go into research at the graduate level. This major will give you data and computational skills and specialized training in transportation systems and human travel behaviour. These skills can help graduates pursue impactful roles including: 

  • Infrastructure Design Engineers: Engineers who create and manage transportation networks like roads and bridges 
  • Urban Planners: Help develop smart and sustainable city transportation systems  
  • Data Analysts: Optimize traffic flow and implement intelligent transportation technologies 

They can also work as policy advisors, consultants, or in environmental roles that help reduce the ecological impact of transportation systems.  

There are also many opportunities in research and academia where students can contribute to innovations and advancements in the field.  

Graduates from this major will be well-equipped for research areas such as travel demand and behavioural modeling, transportation data science and AI, traffic flow theory and control, public transit planning and operations, freight and logistics analytics, sustainable and equitable mobility policy, transport economic and public policy, and finance.   

Potential employers for graduates include:  

  • Car companies  
  • Management consultants  
  • Transportation and logistics companies  
  • Municipalities  
  • Public transportation organizations 
  • And more 

Chair of the Transportation Systems Engineering Major 

Professor Khandker Nurul Habib
Photo of Professor Khandker Nurul Habib [Source]

Professor Khandker Nurul Habib

Professor Nurul Habib teaches in the Department of Civil & Mineral Engineering. He completed his B.Sc. in Civil Engineering and M.Sc. in Civil & Transportation Engineering at the Bangladesh University of Engineering and Technology before receiving his PhD in Civil Engineering from the University of Toronto. In 2025, he was recognized as one of Elsevier’s World’s Top 2% Scientists.  His current research interests include travel demand modelling and transportation planning.  

Courses in Year 1 and Year 2 That Relate to Transportation Systems Engineering   

Summer student tip: 
When autumn starts, it might be easy to forget why some things are necessary and to feel unmotivated. Reminding yourself how each of the new skills you learn will help you in your future career can be a great way to stay focused. 

Year 1

Praxis I and II build a great foundation for solving problems in teams. In past years, students in both courses have had a say in choosing the opportunity they work on. For example, in Praxis II, teams choose a community they are most interested in, which could include a transportation-related community. A few years ago in Praxis I, students explored the “Splartz” (the Praxis term for an opportunity) of improving head support for passengers sleeping on Toronto subway seats.

These courses provide a strong programming and computational foundation that can be applied to almost every area of transportation engineering. These skills are useful for traffic simulation and modelling, working with large datasets, optimizing transit routes and schedules, and data analysis and visualization. You will also build similar computational skills in ESC103: Engineering Mathematics and Computation, where you’ll work on mathematical programming.

And of course, the skills you develop in your math courses (ESC194, ESC195, ESC103, MAT185) will serve as a strong foundation for everything you do. 

Year 2

Engineering and Society helps students incorporate the social, ethical, and human impacts of transportation design and policy into their work. This course reinforces how engineers must consider more than just technical performance when designing transportation-related solutions, as transportation systems directly impact accessibility, sustainability, equity, and safety. This course helps students develop the communication and ethical reasoning skills needed to evaluate how technologies like intelligent transportation systems and autonomous vehicles may impact different communities.

The probability and statistics courses provide the foundation for many Transportation Systems Engineering courses, particularly those focused on data analytics, safety analysis, and intelligent transportation systems. Concepts from MIE286 prepare students to analyze transportation datasets, make models and predictions, and evaluate system performance. Statistical methods are directly applied in courses like CIV335H1: Transportation Safety Analytics and Design and CIV334H1: Transportation Data Analytics – Advanced Statistics and Machine Learning.

Praxis III prepares students for the two collaborative design project courses by developing the teamwork, communication, and systems design skills needed to tackle the engineering problems presented in these courses. The process of identifying an opportunity, developing a complex design solution, and communicating and justifying design decisions mirrors how students will create effective and innovative solutions to complex, multifaceted transportation design problems.

Interesting Courses in This Major  

The core courses focus on data analytics, optimization and simulation methods, transport system planning and operations, and economics and design. Technical electives let students explore other topics relating to transportation like robotics, sustainability, supply chain management, urban systems, and travel behaviour. We encourage you to see what courses and elective options most interest you. Please note that the major and individual course listings will not appear in the academic calendar until July, so you may not be able to find them there yet.  

CIV334H1: Transportation Data Analytics – Advanced Statistics and Machine Learning

This course provides an in-depth exploration of transportation data analytics, focusing on advanced statistical techniques, artificial intelligence, and machine learning methods. It combines theoretical foundations with real-world case studies, allowing students to develop the skills needed to analyze and derive insights from complex transportation datasets.

CIV335H1: Transportation Safety Analytics and Design

This course explores transportation safety analytics with a focus on fundamental principles, geometric design considerations, crash prediction, and safety performance measurement. Students examine driving behaviour, the integration of autonomous transportation systems, and human-machine interaction as critical factors in enhancing transportation safety.

CIV336H1: Fundamentals of Intelligent Transportation Systems and Traffic Management

This course focuses on techniques for optimizing the performance of transportation systems, with an emphasis on traffic networks in congested urban areas. It introduces the fundamentals of Intelligent Transportation Systems (ITS) engineering while covering topics such as the history of ITS, ITS system architecture, transportation control theory, static and dynamic transportation network analysis, and the application of artificial intelligence in ITS.

CIV470H1: Collaborative Design Project II

In this capstone design course, students work in teams to apply their technical knowledge and communication skills to design a solution for a transportation operations problem. Students learn to prepare a professional operational design proposal and formulate a mathematical representation of the operational design problem.

Where To Get Some Experience Before Deciding? 

University of Toronto Rocket Riders – The Student Transit Forum  

The University of Toronto Rocket Riders is a student club for anyone interested in public transit, transportation systems, and urban mobility in Toronto. Inspired by the TTC slogan “Ride the Rocket”, the club brings together students through transit-oriented events, discussions about transit in the university community, and advocacy initiatives about improving transportation in the city.  Rocket Riders offers a fun way to explore real-world transit challenges and connect with students who are passionate about urban transportation and infrastructure. Visit the club page to learn more and follow their Instagram page.   

Sustainable Engineers Association  

The Sustainability Engineering Association (SEA) connects students with opportunities to learn about and contribute to sustainable solutions through workshops, industry tours, mentorship programs, competitions, and networking events. SEA explores topics such as sustainable infrastructure, transportation, energy systems, and policy while helping students build connections with industry professionals. Participation in SEA can help students develop a deeper understanding of sustainable mobility, transportation planning, and the environmental challenges shaping the future of transportation systems. 

UTMIST 

UTMIST is a student-run organization focused on artificial intelligence, machine learning, and data-driven problem-solving. Through technical workshops, projects, and collaborative teams, the club gives students hands-on experience working with modern AI tools and analytical methods. 

You can also do transportation engineering related research. If that interests you check-out Mobility Network at the University of Toronto and University of Toronto Transportation Research Institute.

Visit the Skule Clubs and Design Teams pages to find more extracurriculars. 

Check out the EngSci majors website here for more info:  

Selecting Your Major

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In your second year winter term of EngSci, you’ll select a major in which to specialize. There are a total of nine majors that cover a plethora of engineering disciplines. Choosing your major can be difficult, but there’s plenty of information to help you make the right decision!   

The Roadmap

Actionable steps in the process of choosing your major

Throughout your first two years in EngSci, you’ll take courses that are relevant to all of our majors, and you’ll learn which areas of engineering excite you the most and where your interests and talents lie.  

You’ll also get to talk to upper-year students and hear what they’re up to in the various majors. 

In second year winter term you’ll attend Major Selection information sessions hosted by each major’s Chair (i.e., the professor who oversees the program). 

Along the way there are lots of chances to learn about each major in detail and talk to upper-years, professors, and staff to inform your choice. 

Major Selection: What You Need To Know

Watch your academic advisors, Stephen and Irma, answer some of the most commonly asked questions about major selection and debunk common myths about the process.

Some Common Myths

Selecting your major is important, so let’s dispel some common myths: 

All EngSci majors are open to all EngSci students provided they maintain a clear academic standing as per U of T Engineering guidelines and apply for their major by the major selection deadline. You don’t need to compete with anyone for major spots, and you can select whichever major you want!

Some students believe their entire lives will be dictated by their major. EngSci’s Academic Advisor for Years 3 & 4, Brendan Heath, dubbed this idea as the “golden straight jacket.”
It simply isn’t true!

Yes, each major provides students with the knowledge and skills to work in a specific field, including coursework particularly tailored for that field. However, the wide range of knowledge taught during the foundation years, the overlap in certain topics between majors, the transferable skills developed throughout your extracurriculars, the ability to customize your degree with technical electives, minors, and certificates, and the inherent interconnectedness between engineering disciplines open the door to really diverse career paths (in engineering and otherwise) for EngSci graduates.

An EngSci degree can take you in many different directions, and many alumni have followed career paths that are anything but linear, discovering new opportunities and changing directions along the way.

For example, Thomas Looi graduated in Aerospace Engineering and began his career at MDA before transitioning to medical research. Today, he leads a research group at SickKids Hospital, developing miniature robotic systems for pediatric surgery. Similarly, Vicki Komisar studied Biomedical Engineering, became an assistant professor at UBC, and later transitioned to the federal government, where she now works as a technical advisor.

You’ll see this firsthand at our annual ESEC event where many EngSci alumni with non-linear career paths have shared their stories. Read more about our alumni here.

For more information on the EngSci foundation and upper years check out the EngSci Overview.

Some first-year EngSci students may view the diverse second-year curriculum as an obstacle to specializing in their desired major, since Core 8 students take major-specific courses starting in second year.

While this may result in you learning certain concepts later than your Core 8 counterparts, remember: Core 8 students may be taking specialized courses earlier, but you’re learning things in second year that they aren’t!

EngSci’s Foundation Years curriculum is broad for a reason. It is designed to teach you strong fundamentals in math, physics, and design, while also exposing you to topics in a variety of engineering disciplines. This gives you an incredibly valuable interdisciplinary perspective and sets you up well for working on complex challenges that require people from engineers from different fields to work together.

To compare the Year 2 EngSci and Core8 currcula, let’s look at ECE as an example. EngSci courses ECE253, MAT292, ECE259, MIE286, and ESC204 are similar to Core 8 ECE courses. Furthermore, every other EngSci course has deep connections to ECE, providing a strong understanding of many broad yet but relevant concepts.

Alternatively, say you’re interested in a major such as MSF and but worry that some of the second-year curriculum won’t be relevant to your career. On the contrary, having knowledge of various other fields will put you at an advantage when applying for jobs. Finally, you’ll very quickly catch up with all of your major-specific courses in third year.

Tips for Choosing Your Major

We understand that many of you have already given a lot of thought to major selection. However, even if you feel confident in your current choice, we encourage you to keep an open mind—many students discover new interests in first and second year! By the major selection deadline, you may be even more confident in your original choice. Alternatively, you may have discovered an entirely new area of interest and choose something completely different.   

So, to aid your exploration, here are some tips from those who came before you:  

Explore the Majors

Make sure you know what each major is actually about! Many students have misconceptions about the majors and think they know what they are based solely on their names or something they heard. The EngSci website has handy overview pages for each major. Even if you THINK you’re not interested in all the majors, read through them all.  You might be surprised by what you find! 

Each page has:

  • An overview of what this major is really all about and they types of work it can lead to 
  • An overview of topics covered 
  • A list of sample courses 
  • FAQs about the major 
  • Info on where grads have ended up 

You might be surprised by what you learn!

Your Interests

Identify what areas of engineering interest you. For instance, when looking at a machine, are you more curious about the forces experienced by the physical parts or do you wish you could look through the code that controls its behaviour? Subsystems of machines will almost always directly relate to one or more specific types of engineering, which can help you figure out where your interests lie. 

Courses you Enjoy

VS

Courses you Excel at

Foundation year courses provide a strong background regardless of your chosen major and can help you decide which major suits you best. For example, if you enjoy ECE159, the Electrical & Computer Engineering (ECE) major may be a good fit for you. However, it’s important to also consider the courses where you excel. These may or may not align with your interests. Finding a balance between what you enjoy and what you excel at is important as you prepare for your future career in your chosen major. 

Join Design Teams

While design teams aren’t mandatory, joining at least one can be a great way to gain hands-on experience in your preferred engineering field while having fun. Typically, you’ll join a sub team within the larger team that specializes in a certain area, such as mechanical, electro-mechanical, or software. Working on longer-term projects can help you confirm if a related major aligns with your career goals and provide valuable experience to showcase when applying for jobs in industry.  

ESEC

Every year, the Engineering Science Education Conference (ESEC) is held exclusively for EngSci students, providing a unique chance to meet with leaders from various engineering sectors. Listening to their unique career stories and diverse experiences can help you discover your own passion – and maybe even make you consider a major you hadn’t considered before. It’ll also show you that EngSci graduates’ career paths aren’t linear and that your choice of major doesn’t mean you’ll only be able to work in that field. 

Friends & Family in the Industry

Reach out to friends and family working in industries you’re interested in. Hearing their career stories and discussing your ideas with them might help you decide and establish some connections in the industry at the same time.  

Do Your Research

Once you have a shortlist of majors, it’s time to do some research. As with all research, make sure your sources have credibility. In other words, don’t get your info from fellow 2nd year students. 

Look into the courses offered in each major — do they get your excited?  Check out professors who are doing related research — does it sound interesting? Consult professor and the Engineering Career Centre about job prospects. Reach out to our alumni network to talk to people who are working (and hiring) in the sector right now.

Talking to upper years in your preferred major can also be a great way of getting advice, understanding the workload, and discovering career paths that you may not have considered. 

Talk to Your Profs and TA’s

They’re fully tapped in and can share things you may not have considered about our majors and future careers. 

Talk to Your Advisors

If you’re considering multiple majors, it’s always good to discuss your plans and get a second perspective. While discussing with peers and upper-years is valuable, consulting your Academic Advisors, Stephen or Irma (Year 1 & 2) is especially helpful since they’ve helped many students before you choose their paths and have seen where those choices lead. Towards the end of your second year, you can also reach out to your Year 3 & 4 Academic Advisor Brendan if you have specific questions about the majors you’re considering, such as, courses and electives. Additionally, if you have a specific interest in a niche industry, your advisors can help you align your studies with your career goals. 

Electrical and Computer Engineering

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What is Electrical and Computer Engineering (ECE)

Electrical and Computer Engineering (ECE) underpins the foundation of many of the modern technologies we use every day. ECE sits at the core of all information computation and transmission as well as being central to the most useful form of energy: electricity!  Electrical and computer engineering integrates concepts such as signals, materials science, power systems, programming, computer science, and computer hardware into a single field. The ECE major offers opportunities in a diverse range of industries and research areas; ECEs create signal processors for wireless systems, tools for  medical diagnostics and imaging, control systems for automated manufacturing, consumer electronics, high-speed communication systems on Earth, underwater, and in space, and more!  

ECE provides fundamentals and depth across several sub-disciplines:

the study and engineering systems that generate and transmit photons, including lasers and high-speed photonic transmission systems, which form the backbone of the internet.

the design of analog and digital integrated circuit chips.

the materials, chemical, physical and electrical fundamentals of the computer ‘chip’ industry, and related industries.

the theory and principles that underpin dynamic systems, including robots, aircraft, spacecraft and large-scale manufacturing.

the theory and practice of the connectivity that brings the world together through wireless and wired networking, cellular and high-speed local and global communication.

the reception and manipulation of signals – both analog and digital, including the fundamentals of AI computation.

the theory and practice of dealing with the physics and engineering of wireless signals, which are also used as an analytical system.

the study and engineering of large-scale electrical energy generation, transmission and storage, as well as small-scale energy harvesting and conversion.

the design of large-scale digital and computer systems at the architectural level, as well as at the implementation level.

the science and engineering behind the development and understanding of software systems, including the use of (rapidly evolving) AI in software development.

The major offers a broad range of technical electives. Courses are taught by world-renowned professors from U of T’s Department of Electrical & Computer Engineering and the Department of Computer Science – two of the largest and top-ranked departments in Canada. Students have access to advanced facilities and close research collaborations between professors and global partners, including the Fujitsu Co-Creation Research Laboratory. Students also benefit from the university’s affiliation with organizations like the Vector Institute, U of T’s SciNet supercomputing consortium, and the vibrant tech and startup landscape in Toronto. 

Why Choose ECE? 

Why Choose This Major?

You’re interested in:

  • Everything relating computers, including both the hardware and software sides
  • Research related to electricity and magnetism, on topics such as superconductive materials, wireless systems and signals, and electromagnetic radiation
  • Being on the leading edge technology such as self-driving cars, personal electronics, and more
  • Learning and participating in Quantum computing and Quantum Communication from the physics side as well as the software
  • Modern technology such as self-driving cars, personal electronics, and more
  • A flexible major that will allow you to enter almost any field you want and has a diverse range of applications across nearly every industry
  • Creating a cutting-edge tech startup with an impact upon the world

EngSci ECE is quite different from the Core 8 Computer Engineering and Core 8 Electrical Engineering majors. In EngSci, the foundation years enable you to learn more advanced topics later. Furthermore, the core courses in EngSci ECE cover fundamentals of both the EE and CE majors, so that Eng Sci ECEs have greater breadth across the entire ECE field.

Where Can This Major Take You?

Recent EngSci ECE graduates have pursued graduate studies at top universities such as: 

  • Carnegie Mellon University
  • Cornell University
  • Columbia University
  • MIT
  • Stanford University
  • UC Berkeley
  • University of Toronto
  • University of Waterloo

Sample employers for recent ECE graduates include:

  • AMD
  • Apple
  • Google
  • McKinsey & Company
  • Meta
  • RBC
  • Toronto Hydro
  • Cerebras  
  • Tenstorrent 

EngSci ECE graduates have also started companies such as SoundHound, Ergeon, Medchart, and Databricks.

Upper-Year Insights

Rishabh Iyer
EngSci ECE 2T4 + PEY, Summer Researcher @ U of T, Electrical Lead @ Blue Sky Solar Racing

“The EngSci ECE major is structured such that you get a broad exposure to various subfields within the discipline. In my third year, I was required to take core courses that covered every fundamental aspect of ECE, giving me a [deep and broad] understanding of the field. Having the ability to appreciate a system at all its different levels – from the semiconductor level to the hardware and up to the software level – has been perhaps the most rewarding experience for me. This holistic understanding allows me to see how each component and layer interacts and contributes to the overall functionality of a system.”

“One of my favorite courses was ECE350 (Semiconductor Electronic Devices). These devices are the fundamental building blocks for almost all the electronics that we use. I find the intricate and complex design of these nanometer-sized structures incredibly fascinating.“

Chair of the Electrical and Computer Engineering Major 

Professor Rose
Picture of Professor Jonathan Rose

Professor Jonathan Rose 

Professor Jonathan Rose was the Chair of the Department of Electrical & Computer Engineering and has taught EngSci students for many years. He was a co-founder of Right Track CAD Corporation which delivered FPGA chip-level architecture and CAD tools to customers, and was acquired by Altera, now Intel. His current research focuses on software and natural language processing for mental health diagnosis and therapy, as well exploring Large Language Models at the conceptual level. 

Interview with Professor Rose

Courses in Year 1 and Year 2 That Relate to Electrical and Computer Engineering

Year 1

ESC180 will be your first programming course in university. This course gives you an introduction to programming using Python, which will open up the world of computer software.

ESC190 will be your second programming course. This course introduces the C programming language, which is much more low-level; as you learn C, you’ll learn more about computers themselves, including memory management and runtime complexity, as well as many algorithms and data structures found in modern software.

ECE159 will start from the basics of circuitry such as DC circuit analysis with different methods, before eventually leading to more intermediate topics such as Op-amps, transient circuit analysis, and AC circuits. The practicals are very hands-on and will require you to build many interesting circuits and analyze them with a variety of electrical measuring instruments. Combined with the theory-focused lectures, this course gives you a strong foundation for the hardware side of ECE.

Year 2

ECE253 combines features of circuits with programming, bridging the gap between the small electrical components that build computers and the programming we use the components for. You’ll learn everything from basic logic circuits to logic computation to computer processors. You’ll also learn to program simple processors in the ultra-low-level Assembly language.

AER210 combines two concepts. The first half of the course is an extension of Calculus II and focuses on vector calculus, which is math in higher dimensions. Electrons, wires, insulators, and other objects in electronics exist in three dimensions, so this math is crucial.

The second half of the course covers fluid mechanics, which is the study of the motion of fluids (liquids and gases). Many things in fluid mechanics are analogous to things in electricity. For example, conservative fields appear in both fluid mechanics and electric field theory.

ECE259 combines fundamental physics with useful techniques from vector calculus to explore features of electricity like electric force, voltage, current, and field strength.

Interesting Courses in This Major 

ECE360: Electronics  

This course introduces the fundamentals of electronics, covering the analysis and design of basic electronic circuits. Topics include introductory frequency-domain analysis, operational amplifiers, diodes, field-effect transistors, bipolar junction transistors, small-signal analysis, and single-stage amplifiers, along with practical experience using circuit analysis techniques.

ECE318: Fundamentals of Optics  

This course explores the fundamentals of optics, including geometric optics, polarization, interference, diffraction, and Fourier optics. Topics include optical imaging systems, polarized light, interferometers, thin films, diffraction gratings, and basic optical signal processing. 

ECE435: Quantum Computing Hardware  

This course explores the engineering of quantum processors, covering quantum computing fundamentals, superconducting and semiconductor spin qubits, quantum hardware design, fabrication and characterization techniques, and the modelling, simulation, and testing of qubits and their control and readout systems. 

ECE532: Digital Systems Design 

This course covers practical applications of advanced topics in digital systems design, such as embedded processors, hardware/software interfacing and interactions, software drivers, embedded operating systems, and much more. You’ll implement significant design projects on FPGA development boards. 

See the full course listing for each EngSci major in the academic calendar.

Where To Get Some Experience Before Deciding? 

There are so many clubs involving ECE that we couldn’t list them all. For example, almost all design teams have sub teams for circuitry and programming, so if you’re interested in ECE, you can join just about any design team and get relevant experience. Your choices can include software and AI-focused teams that’ll give you experience with programming. Here’s a short list of design teams, all of which have strong ECE components.   

Visit the Skule Clubs and Design Teams pages to find more extracurriculars. 

Check out the EngSci majors website here for more info:  

Robotics Engineering

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Don’t anthropomorphize robots. They hate it when you do that.

What is Robotics Engineering?

Robotics Engineering is the study of robotic systems, combining circuitry, mechanical design, computer algorithms, and control systems to develop advanced mechatronic systems. Robotics Engineering combines several fields, including aerospace engineering, electrical and computer engineering, mechanical engineering, computer science, and material science. Robotics engineers work on a diverse set of technologies, such as self-driving cars, personal electronics, space exploration rovers, large-scale automated logistics systems, and precise robots for minimally invasive surgery. The robotics engineering field and market is in an exciting period of growth and diversification.  

The University of Toronto Robotics Institute is home to the largest and most diverse robotics research program in Canada and unites robotics experts from across the university around the research pillars of autonomous field robotics, healthcare robotics, and advanced manufacturing. Faculty members include Canada Research Chairs in robotics, machine learning, and image analysis.  

Professor Aryan Rezaei Rad with the newly installed robotic arm. (Photo by Phill Snel) [Source]

Why Choose Robotics Engineering? 

Why Choose This Major?

You’re interested in:

  • Everything to do with robots, including hardware and software, 
  • Working with a vast range of applications, such as aerospace, healthcare, transportation, personal electronics, and more, and 
  • Creating a cutting-edge tech startup that impacts the world.  

In Robotics Engineering, you’ll be taught by world-renowned faculty members from the University of Toronto Robotics Institute, the University of Toronto Institute for Aerospace Studies, and the Departments of Electrical & Computer Engineering, Mechanical & Industrial Engineering, and Computer Science.  

Where Can This Major Take You?

Recent EngSci Robotics Engineering graduates have pursued graduate studies at top universities such as:

  • Carnegie Mellon University
  • ETH Zurich
  • MIT
  • UC Berkeley
  • University of Michigan
  • University of Oxford 
  • University of Toronto

Sample employers for recent Robotics Engineering graduates include:

  • AMD 
  • Applanix 
  • AXIBO 
  • Geeral Motors 
  • Zebra Technologies 
  • Google 
  • Intel 
  • Qualcomm 
  • Boston Dynamics 

Robotics Engineering Major Chair  

Professor Kelly
Picture of Professor Jonathan Kelly

Professor Jonathan Kelly 

Professor Kelly is a Professor at the University of Toronto Institute for Aerospace Studies, Director of the Space & Terrestrial Autonomous Robotic Systems (STARS) Laboratory, and Chair of the Robotics Major at the University of Toronto. Before joining U of T, he was a Postdoctoral Associate at MIT’s Robust Robotics Group. He completed his Ph.D. in robotics at the University of Southern California. His research focuses on autonomous robotic systems capable of operating reliably in challenging environments, including space and remote terrestrial settings. He is also interested in applying space robotics technologies to real-world terrestrial robotic systems. 

Interview with Chair of the Robotics Major 

Check out an interview with Professor Jonathan Kelly, the chair of the Robotics major.

Courses in Year 1 and Year 2 That Relate to Robotics Engineering

Year 1

ESC180 will be your first programming course in university. Your programming skills will help you design the “brain” of your robots.

ESC190 will be your second programming course. This course introduces the C programming language, which is commonly used for interacting with hardware components. This course focuses on implementing various algorithms, which are used for completing various real-world tasks such as pathfinding.

ECE159 will help introduce you to circuitry, which you’ll need to connect the physical systems with the “brains” of your robots. The practicals involve hands-on experiences in which you build and measure the properties of your own circuits. Combined with the theory-focused lectures, this course gives you a strong foundation for all your future ECE courses in Robotics.

PHY180 will cover concepts such as kinematics, dynamics, and interactions within systems. This course will provide a foundation for understanding further advanced physics concepts such as forward and inverse kinematics, which explain robot movement and interactions.

ESC103 will introduce the basics of linear algebra. You’ll use this knowledge, along with that gained from MAT185, in upper-year courses such as Dynamics and Introduction to Robotics. Robotics concepts such as rigid body movement and circuitry are described using matrices. Much of the computing a robot does in its operation is also implemented as linear algebra through code, in programming languages you’ll learn in ESC103.

ESC101 and ESC102 will require you and your team to tackle a real-world engineering opportunity. Although your opportunity and approach towards it will vary, you may have an opportunity to integrate robotics in your solutions.

Year 2

ECE253 bridges the gap between the electrical components that build computers and the programming we do with them. You’ll learn basic logic circuits, logic computation and functions of a simple computer processor. Along the way you’ll learn to program simple processors in the low-level Assembly language. You’ll use some of these principles in upper-year courses.

AER210 combines two concepts. The first half of the course is an extension of Calculus II and focuses on vector calculus; this branch of math is crucial to understanding robot movement. The second half of the course focuses on fluid mechanics, which is the study of the motion of fluids (liquids and gases); this will be useful when designing robots to be as aerodynamic as possible.

ESC204 integrates all your technical and design knowledge into a course-long mechatronics design project based on the United Nations Sustainable Development Goals. You’ll learn a lot about building robotic systems for impactful applications.

Interesting Courses in This Major

CSC384 Introduction to Artificial Intelligence

This course covers the theories and algorithms that cover a large part of the basis for artificial intelligence. The specific topics include decision-making under uncertainty, learning, classical automation, and logical representations and reasoning. You’ll cover both practical programming applications and theory. 

ROB521 Mobile Robotics and Perception

This course covers the fundamentals of mobile robotics and sensor-based perception. These topics are applicable in self-driving cars, space exploration, unmanned aerial vehicles, search and rescue, and much more. Topics include sensors, localization, mapping, route planning, path tracking and software frameworks. Labs in this course use a mix of software simulations and hardware. This course will be applicable for building any autonomous system. 

ROB498 Robotics Capstone Course

In this course, students apply technical knowledge to solve a challenging real-world robotics problem. Supported by the teaching team comprised of domain experts, students work in groups and have considerable freedom in developing a complete robotic hardware and software system based on the “sense-plan-act” framework. 

Student-built drone from the ROB498 course

See the full course listing for each EngSci major in the academic calendar.

Where To Get Some Experience Before Deciding?

Many extracurriculars offer opportunities to engage with different areas of robotics. Lots of design teams have a circuitry team, programming team, and/or a mechanical design team, so joining any of these would be a great way to gain robotics experience. There are also software and AI-related opportunities to give you experience with programming for robotics. We’ve listed a few that you can check out, but you’ll learn about even more once you get here. 

U of T Robotics Association (UTRA)

Founded in 2004, UTRA has built robots for all kinds of purposes. Their teams include Sumo, RoboSoccer, Combat, Pacbots, Robonars workshops, and an annual hackathon called UTRAHacks. If you’re considering the Robotics major, joining one of these teams or sub teams will allow you to explore your specific interests within Robotics. Check out their website to learn more about their teams and how to get involved. 

Robotics for Space Exploration (RSX)

RSX designs, builds, and tests robots for planetary exploration. They compete in space engineering competitions around the world, notably the International University Rover Challenge (URC) in Utah and the CanSat competition in Texas. Furthermore, they host SEEK (Space Exploration and Engineering Kompetition), which is an annual competition organized by RSX where students gain practical experience with space technologies. Whether you’re interested in the mechanical, electrical, or software aspect of robotics, RSX will have a sub team for you. 

aUToronto Autodrive

aUToronto is a student design team dedicated to building a self-driving car. The team placed first overall at the 2025 SAE AutoDrive Challenge™ II. Currently, they are working towards a Level 4 autonomous vehicle capable of complete navigation in urban driving environments to compete in Round II. Whether you’re interested in mechatronics & infrastructure, control systems, or autonomous vehicles in general, apply to aUToronto.

Visit the Skule Clubs and Design Teams pages to find more extracurriculars. 

Check out the EngSci majors website here for more info:  

Engineering Physics

Posted on by orientation

Q: Why is it best to teach physics at the edge of a cliff?

A: Because that’s where students have the most potential.

What is Engineering Physics?

The Engineering Physics major prepares students to apply cutting-edge research in physics and engineering to innovations in modern technologies. Engineering physicists work across a variety of industries, developing instruments for use in experiments (such as a gravitational wave observatory) or devices that harness physical phenomena (such as advanced nanomaterials for solar energy, quantum computers, and cancer therapies). They may model complex natural phenomena, from the inner workings of cells to the formation of entire solar systems.  

The Engineering Physics major is suited for those with a strong interest in pure or applied physics who see its creative possibilities. It provides students with both specialized physics and engineering courses. Having been a part of the EngSci program for almost six decades, Engineering Physics has a long history of innovation and successful graduates. In fact, Engineering Science itself used to be called “Engineering Physics.” 

Engineering Physics includes specialized physics and engineering design courses. Courses cover concepts from theoretical and applied physics to pure and applied math and computer science. They’re taught by professors from U of T’s departments of Physics, Mathematics, Chemical Engineering & Applied Chemistry, Electrical & Computer Engineering, and more.  

Photo by Dan Cristian Paduret on Unsplash

Why Choose Engineering Physics? 

Why Choose This Major?

You’re interested in:

  • Particle physics, cosmology, quantum optics, planetary physics, theoretical physics, mathematics, and more
  • Combining physics and engineering design in fields such as optics, energy generation, astrophysics, electronics, climate, geophysics, economics, and more
  • Research! Physics is a field that is always rich in researchers and research topics, both theoretical and experimental. In Engineering Physics, you’ll learn about recent experiments regarding current theories. Your coursework will provide an excellent foundation for graduate studies.
  • The “Science” part of “Engineering Science”

Many fields and industries require physics where you might not expect it. Engineering physicists might work at environmental agencies to develop models of complex systems, like Earth’s atmosphere. Furthermore, the fields of econophysics and quantitative finance are growing rapidly as financial companies recognize the usefulness of math and modeling from physics in predicting systems like the stock market. 

Where Can This Major Take You?

Recent EngSci Engineering Physics graduates have pursued graduate studies at top universities such as:

  • Cambridge University
  • Carnegie Mellon University
  • Cornell University
  • Harvard University
  • MIT
  • Stanford University
  • UC Berkeley
  • University of Toronto

Sample employers for recent Engineering Physics graduates include:

  • AMD
  • Citigroup
  • HP
  • MDA
  • McKinsey & Company
  • RBC

Courses in Year 1 and Year 2 That Relate to Engineering Physics

Work in modern physics requires a large skillset; almost every course in first and second year will provide you with some necessary skills for Engineering Physics. Below are some brief overviews of how each course relates to this major. 

Year 1

PHY180 will introduce you to classical mechanics, which can describe anything on a human-sized scale. The principles of classical mechanics, such as energy and momentum, are also frequently used in modern physics. Furthermore, the semester-long pendulum lab report is a great introduction to physical experimentation and scientific writing.

MSE160 is divided into two parts. The first half of the course will cover fundamentals of molecular science such as electrons, photon emission, the electromagnetic spectrum, and crystal structures of materials. The second half will discuss material properties derived from classical mechanics, such as stress, shear, and tension (which you would have first encountered in CIV102).

CIV102 applies the physics of materials and static systems in structural design. The questions you’ll see on assessments involve solving systems with many unknown variables, which is common in physics.

ECE159 will start from the basics of circuitry, eventually covering more advanced circuit analysis techniques. Electricity is a fundamental force in physics; this course provides a strong foundation for future coursework in the field. Through the hands-on labs, you’ll learn how to build certain types of circuits and use various electrical measuring instruments.

What would math be without calculus? ESC194 and ESC195 will cover a lot of calculus from a proof-based approach, which will provide an excellent foundation for future calculus courses. Calculus is the most important field of math for physics!

ESC103 and MAT185 will introduce you to the basics of linear algebra, and computational programming with MATLAB. Linear algebra is used all over physics, such as in Hermitian matrices in quantum mechanics, which you’ll learn about in second year. Computational programming is one of the most useful skills you can have for research or modeling, especially for physics.

ESC180 will introduce you to computer programming in Python, which is commonly used for scientific computing and machine learning (both of which are important to an engineering physicist). ESC190 will introduce you to C, a low-level programming language better suited for embedded programming and high-performance code. The course focuses on data structures and algorithms, which can help solve complex real-world problems.

ESC101 and ESC102 take you through the entire engineering design process, from research, prototyping, testing, and verification. While these courses may not involve very complex math and physics, they’ll expose you to common practices in the development of experiments, devices, and instruments. For example, Praxis I and II will require you and your team to conduct scholarly research into engineering opportunities, reference designs, and design decisions. Furthermore, you’ll be required to verify the validity of your solutions through codes, standards, and testing, approximating rigorous industry-standard testing practices for your own purposes.

Year 2

PHY293 covers waves and the basics of general relativity. In physics, you can model objects and phenomena as waves; this course gives you the mathematical tools to do so. Its introduction to general relativity is essential, since the two largest branches of physics today are quantum mechanics and general relativity.

PHY294 is divided into two halves, with quantum mechanics and thermal physics in the first and second halves, respectively. Both fields are essential in modern physics. The quantum mechanics part covers mathematical theory and the crucial experiments that resulted in important observations in quantum mechanics. The thermal physics part covers statistical mechanics and gas laws.

CHE260 is another two-part course, where both halves are built upon basic chemistry and classical mechanics. The thermodynamics half covers energy, heat, work, and entropy. The heat transfer half covers conduction, convection, radiation, and how an object’s geometry and material can affect the rate at which it heats up and cools down.

ECE259 combines fundamental physics with useful techniques from vector calculus to explore features of electricity like electric force, voltage, current, and field strength.

AER210 is another two-part course which extends your calculus knowledge from first year. In the first half, you’ll extend your calculus knowledge into 3D and learn about multiple integrals and vector calculus. In the second half, you’ll study fluid mechanics and apply your knowledge in areas such as dimensional analysis, hydrostatics, and viscous flows. You’ll also conduct two hands-on laboratory experiments involving microfluidics and flow visualization.

MAT292 will build upon the differential equations you learned in Calculus I. You’ll see how important differential equations are to physics through the various examples presented in the course.

MIE286 will introduce you to the fundamentals of probability and statistics. MIE286 will provide you with the tools you need to begin studying statistical mechanics, one of the most important fields in modern physics with wide applications to quantum mechanics. Statistics and probability are also of deep interest in experimental physics, especially when considering the validity of an experiment’s results through error and uncertainty.

Interesting Courses in This Major

In Engineering Physics, you’ll have a large selection of technical elective courses with which you can customize your degree. You can study topics including theoretical physics, electrical and computer engineering, and more. There are two types of courses in this major: Group A courses (which apply physics and math fields such as artificial intelligence, computer hardware, and energy) and Group B courses (which involve topics such as theoretical physics and Earth science). In Engineering Physics, you must take a certain number of courses from both Groups. Engineering Physics is often considered one of the more flexible Engineering Science majors, but flexibility alone is not a good reason to choose it. The major is best suited to students who genuinely love physics, since you’ll spend a significant portion of your degree studying the subject in depth.

PHY327: Advanced Physics Laboratory I (Group A)

This course will introduce you to modern experimental research, focusing on different instrumentation used in physics experiments. In addition to the standard set of experiments, which include molecular, atomic, nuclear, and particle physics, there are a limited number of research projects available. 

PHY483: Relativity Theory I and PHY484: Relativity Theory II (Group B) 

PHY483 will introduce you to Einstein’s theory of relativity. You’ll learn about gravitational physics and general relativity, starting from solutions of Schwarzschild, Kerr, and more. PHY484 will apply general relativity to astrophysics and cosmology, introducing black holes and the large-scale structure of the universe. 

PHY492: Advanced Atmospheric Physics (Group B)

This course prepares you for research in atmospheric physics. Themes may include techniques for remote sensing of the Earth’s atmosphere and surface, atmosphere-ocean dynamics, the physics of clouds, precipitation, and convection in the atmosphere. 

AER507: Introduction to Fusion Energy (Group A)

 This course will cover the basic physics of fusion reactions, which is highly relevant to sustainability: it forms the basis of an essentially inexhaustible energy resource. Nuclear reactions are the energy source for stars, so they could form the basis of an inexhaustible fuel source on earth. Topics include reaction cross-sections, particle energy distributions, Lawson criterion and radiation balance, plasma properties, plasma waves, plasma transport, heating and stability, and fusion plasma confinement methods. 

See the full course listing for each EngSci major in the academic calendar.

Beyond First Year

University of Toronto Aerospace Team (UTAT)

UTAT is an exciting, award-winning, and record-breaking design team comprising undergraduate and graduate students working on amazing design projects in the aerospace field. Their divisions include Aerial Robotics, Rocketry, Space Systems, Unmanned Aerial Vehicles, Aerospace Policy, and Outreach. You can work in a variety of subdivisions, such as propulsion, aerodynamics, and autonomy. If you’d like to join UTAT, attend one of their many recruitment events or simply reach out to the director of the division/portfolio which most interests you! 

U of T Human-Powered Vehicles Design Team (HPVDT)

HPVDT focuses on the design and construction of innovative, high-performance human-powered vehicles. Currently, they’re working on a speedbike and a human-powered aircraft. In recent years, their vehicles have broken world speed records! As a team member, you might work on mechanical or electrical computer-aided design (CAD), finite element analysis (FEA), embedded programming, vehicle aerodynamics, microcontrollers and microprocessors, and machining skills. If any of that interests you, feel free to sign up here! 

Astronomy & Space Exploration Society (ASX)

The ASX’s main purpose is to educate and excite people about astronomy and space. ASX holds over 10 events each year with hundreds of attendees; their biggest event is the Annual Symposium, which has attracted up to 500 people. ASX has invited many prominent professionals in astronomy and related fields as speakers, including Canadian astronaut Chris Hadfield!

Visit the Skule Clubs and Design Teams pages to find more extracurriculars. 

Check out the EngSci majors website here for more info:  

Aerospace Engineering

Posted on by orientation

Why was the aerospace engineer always calm during turbulence? 

They knew how to stay grounded… 

What is Aerospace Engineering?

Aerospace engineering involves the science, development, and testing of aircraft, spacecraft, missiles, satellites, rocket-propulsion systems, and robotic systems operating within or beyond earth’s atmosphere. In addition, aerospace engineers might work on cars, wind turbines, unmanned aerial vehicles, telescopes, and more.  

Aerospace engineering requires knowledge of mechanical engineering, robotics, computer science and engineering, material science and civil engineering, energy systems, physics, and more. As a result, graduates of an aerospace engineering program develop a broad foundation across many disciplines, making them well-rounded engineers who are equipped to work on diverse engineering problems. There is exciting work being done such as research in autonomous flight, superlight materials, experimental energy sources, and low-cost space travel. You’ll enter a technologically advanced and challenging field, where you’ll be responsible for advancing human exploration and transportation on earth and beyond.  

The Aerospace Engineering major offers a comprehensive curriculum encompassing dynamics and aerodynamics, control systems, structures, propulsion, robotics, fusion energy, and space systems design. It provides instruction on both aircraft and spacecraft design and flight, emphasizing fundamental science and engineering principles. Courses also cover topics such as sustainable aviation, environmental considerations, and space exploration, and you’ll have a wide range of technical electives with which you can focus your degree.  

Aerospace Engineering Major Art by EngSci 2T6 Leah Bel Ben-Tzur (instagram: @leah.bentzur)

Why Choose Aerospace Engineering? 

Why Choose This Major?

You’re interested in: 

  • Research areas such as computational and experimental fluid dynamics, with applications ranging from spacecraft to race cars.
  • The science behind propulsion, combustion, and fusion energy.   
  • Aircraft and spacecraft flight systems and controls.  
  • Developing autonomous terrestrial and space robotic systems that can function for extended periods in demanding conditions.  
  • Planes, rockets, drones, satellites, and so much more! 

In the EngSci Aerospace Engineering major, many of your professors will be from the University of Toronto Institute for Aerospace Studies (UTIAS). UTIAS is devoted to aerospace graduate studies and has a long history of innovation and aerospace research with top industry and institutional partners.  

Where Can This Major Take You? 

EngSci Aerospace Engineering graduates have pursued graduate studies at top universities such as: 

  • UTIAS 
  • Caltech 
  • Cambridge University 
  • ETH Zurich 
  • MIT 
  • Stanford University 
  • University of Michigan 

Sample employers for recent Aerospace graduates include: 

  • Space Agencies such as NASA and CSA 
  • Bombardier 
  • MDA Space Missions 
  • Honeywell 
  • Pratt & Whitney Canada 
  • Safran Landing Systems 
  • National Research Council Canada 

EngSci Aerospace graduates have also started companies such as Kepler Communications, Aerovelo, and 2XL Games, and NordSpace.

Upper-Year Insights

Nat Espinosa Quintero
EngSci 2T5 + PEY (Aerospace), Aerodynamics Lead @ UTAT Rocketry

“Getting involved in the aerospace field has been one of the biggest challenges in my career and the steepest learning curve I’ve experienced. After lots of constant effort, choosing this major and being exposed to the industry, I look back and I see how much I’ve grown since I got to my first day of university. Acknowledging every little effort you put into your career and seeing it bloom day by day toward your dreams has been my most memorable experience!” 

“Make sure you really enjoy aviation and/or space! Being passionate about aerospace has definitely made my journey through EngSci Aero the most exciting and challenging experience. This being said, finding yourself a group of friends who share your interests is also important. Don’t be afraid of making connections, develop your social skills and make lots of long-lasting relationships with everyone around you.” 

Chair of the Aerospace Engineering Major  

Professor Alis Ekmekci
Picture of Professor Alis Ekmekci

Professor Alis Ekmekci 

Prof. Ekmekci’s research focuses on topics like flow-induced noise and vibration, flow-structure interactions, unsteady separated flows, flow control, and vortex dynamics. She completed her MASc and PhD in Mechanical Engineering at Lehigh University before joining UTIAS in 2008; she now leads the Experimental Fluids Research Laboratory. Beyond her research, Prof. Ekmekci is a mother of two and is known by many EngSci students for teaching the vector calculus and fluid mechanics course, AER210, in second year.  

Courses in Year 1 and Year 2 That Relate to Aerospace Engineering

Almost everything you learn in the foundation years can relate to the Aerospace Engineering major. For example, as an aerospace engineer, you might design firmware systems for drones or satellites, in which case courses such as ECE159 (Fundamentals of Electric Circuits), ESC190 (Computer Algorithms and Data Structures), and ECE253 (Digital and Computer Systems) will be extremely important. If you’re interested in aerodynamics, then PHY180 (Classical Mechanics) and AER210 (Vector Calculus and Fluid Mechanics) would be especially useful. Below are just a few examples of relevant courses and their applications to Aerospace Engineering. 

Year 1

CIV102 will teach you concepts in structural engineering relating to the design and material selection of strong structures, which directly relate to aerospace engineering. For example, loading a bridge is like keeping a plane wing straight, and vibrations in buildings are like airplane turbulence.

PHY180 covers kinematics, dynamics, and other concepts to provide you with a strong foundation in physics.

ESC103 will introduce you to linear algebra — which is an essential branch of mathematics for aerospace engineering as it relates to structures, electronics, and more. It will also introduce mathematical programming languages, to automate your mathematical computations. MAT185 is a pure linear algebra course which will strengthen your skills from ESC103 and introduce more advanced topics.

Year 2

CHE260 is split into two halves: thermodynamics and heat transfer. In aerospace, a knowledge of thermodynamics is crucial when building engines and dealing with gases. During the heat transfer portion, you’ll learn about how heat moves through materials; a common problem in aircraft design is keeping your materials hot or cold enough when moving through the atmosphere at high speeds. If you’re interested in Aero, pay attention in CHE260.

AER210 is another two-part course. The first half focuses on vector calculus, which involves differentiation and integration in vector fields in 3D space. You’ll use this in the fluid mechanics half of the course, which introduces ways to analyze and predict the motion of fluids in different situations. The principles from fluid mechanics are invaluable for anything to do with aerodynamics, speed, and flight.

MAT292 gives you a solid foundation in modeling different physical systems mathematically with ordinary differential equations (ODEs). For example, heat-related systems in plane engines can be modeled with ODEs.

Interesting Courses in This Major

AER302: Aircraft Flight

This course discusses everything about aircraft flight. Topics include the atmosphere, equations of motion, airspeed measurement, drag, thrust and power, climb, turns, pull-up, takeoff, landing, flight envelope, static stability and control, and dynamic stability.

AER407: Space Systems Design

This course teaches real-world space system design with a hands-on approach, led by engineers from MDA and Microsat Systems Canada. Students work in teams on different aspects like operations, systems, mechanical, electrical, control, and science. The course will include lectures, workshops, and assessments like the Preliminary Design Review and Final Report.

AER515: Combustion Processes

This course takes CHE260 to the next level and goes in-depth into the thermodynamics, chemistry, kinetics, and calculations of combustion. Combustion will also be discussed with respect to rockets, reciprocating engines, gas turbines, furnaces, and the environment.

AER525: Robotics

This course is about analytical robotics and the design and control of industrial robots and their instrumentation. Topics include forward, inverse, and differential kinematics, inverse and forward dynamics, screw representation, statics, motion and force control of robot manipulators, actuation schemes, task-based and workspace design, mobile manipulation, and sensors and instrumentation in robotic systems. Experiments will be held in the Robotics Laboratory.

See the full course listing for each EngSci major in the academic calendar.

Where to Get Some Experience Before Deciding?

Here are a few design teams you might find interesting if you’re considering Aerospace Engineering. However, keep in mind that these are just a small sample of the many clubs, teams, and extracurricular opportunities at U of T: a lot of other teams involve skills and concepts that relate closely to the Aerospace major and are worth exploring.

University of Toronto Aerospace Team (UTAT)

UTAT is an award-winning design team of undergraduate and graduate students working on aerospace-related design projects. UTAT has several divisions that you can join, with Rocketry, Aerial Robotics, UAV (Unmanned Aerial Vehicle), Space Systems, Outreach, and Aerospace Policy. Each division consists of subteams including mechanical, electrical, software, propulsion, control, and much more. There are many ways to get involved with UTAT, so consider joining their team! 

Robotics for Space Exploration (RSX)

RSX designs, builds, and tests robots for planetary exploration. They compete in space engineering competitions around the world, notably the International University Rover Challenge (URC) in Utah and the CanSat competition in Texas. Furthermore, they host SEEK (Space Exploration and Engineering Kompetition), which is an annual competition organized by RSX where students gain practical experience with space technologies. 

U of T Formula Racing (UTFR)

UTFR is an award-winning team that designs and builds an electric formula race car and competes in various Formula Racing competitions around the world. Their subteams develop the electrical, autonomous, and mechanical aspects of the race car; prospective Aerospace Engineering students might want to consider joining the aerodynamics subteam, which is dedicated to making the car go fast. If you’re interested, keep an eye out for their recruiting cycle. 

Visit the Skule Clubs and Design Teams pages to find more extracurriculars. 

Check out the EngSci majors website here for more info:  

MAT185: Linear Algebra

Posted on by orientation

Why were the Wright Brothers linearly independent vectors?

Because two of them made a plane!
Photo by Joshua Sortino on Unsplash

Linear algebra is a field of math that’s used throughout engineering and science. In fact, the first step in solving many engineering problems is to make it a linear algebra problem. It’s no surprise that most engineering and science programs teach linear algebra early on.  

MAT185 is loose continuation of ESC103. It teaches linear algebra from a first principles, ground-up approach. You’ll learn the reasoning behind mathematical ideas and rigorously prove that they’re true. You’ll cover some concepts that were introduced in ESC103, such as vectors, matrices, and differential equations, and new concepts including fields, vector spaces, bases, coordinates, linear transformations, and eigenproblems.  

However, unlike ESC103, there’s little computation in this course. This is a proof-based course, so you’ll be tested on your ability to connect concepts and use linear algebra principles to prove and disprove general statements. MAT185 is taught as if you’ve never taken a proof-based course before, so don’t worry if you’re new to this. You’ll be taught methods like proof by contradiction, proof by induction, proof of contrapositive, proof of equal sets, and proof of if and only if statements. Students have varying experiences with this course. Some find it reasonable while others find it very difficult. There’s little correlation between how you felt about ESC103 and how you’ll feel about MAT185. While they both cover some pure math and linear algebra, the questions you’re asked, the perspective from which you learn, and what you’re expected to understand are completely different.  

Professors

Professor Philipp Seiler
Professor Philipp Seiler [Source]

Professor Philipp Seiler

Professor Seiler will be one of your instructors. He completed his bachelor’s and master’s degrees in mechanical engineering and Mechatronics at TU Braunschweig, Germany, where he also earned his PhD in Materials Science. He held research positions at Purdue University and the University of Cambridge, where he worked on materials under extreme conditions, such as those used in gas turbines, nuclear reactors, and lightweight structures. Before joining the University of Toronto as a professor, he taught advanced manufacturing and mechatronics as an assistant professor at the University of Kent, UK. 

Professor Sean Uppal

Bio coming soon

Professor Interview

Snippets from our interview with Professor Seiler: 

“In my research, […] I don’t think there’s a single day where I don’t use linear algebra.”  

“I have an active teaching style. I like going on academic detours […] I do not plan lectures down to the minute. I come to lectures with a brief outline, then I see how the students follow and react.”

“One by one, I will introduce the necessary concepts for [students] to understand [linear algebra] […] If I were to simply teach how a tool like matrix multiplication works, e.g. just by following an algorithm, students would quickly forget it. By knowing the proofs, you can understand why and how matrix operations work. Even if you forget the details, it will be easier to relearn it. Moreover, I want students to understand why certain concepts are true and why they work. Therefore, proofs can help students understand linear algebra conceptually.”

For more, check out the full Interview Transcript here!  

Course Highlights

  • The course textbook. We don’t want to spoil your fun, so read it for yourself!

  • Not only will you learn new theorems, but you’ll learn how to prove them so that you know they’re true.

  • A lot of math symbols. (Don’t worry, the professors will walk you through them.) 

  • The pure satisfaction you gain from proving difficult mathematical statements by using fundamental linear algebra concepts. 

Week in the Life of an MAT185 Student

Lectures

There are three hours of lecture per week in this course. Lectures cover proofs, explanations of theorems, and concepts. Professor Seiler uploads semi-completed templates of lecture notes before class; you’re encouraged to use them to follow along, filling in blank sections as he teaches. There will be some example questions but ensure you do additional practice in tutorials or on your own time. If you have questions, don’t hesitate to ask the professors.  

Tutorials

There’s one hour of tutorial per week in this course. In tutorials, you’ll be given practice problems and the teaching assistants will help you solve them. For MAT185, these tutorials are helpful as they provide a lot of practice, but it’s only as good as you make it.  

Textbook Questions

There are also recommended textbook questions. Do these. They are not marked and are technically optional but are a great source of practice problems outside of tutorials. Similar questions may appear on tests and exams. If you can’t complete all these recommended problems, don’t worry they can be on the challenging side. Simply try to solve as many as you can. Any practice is good practice. 

Midterms and Exam

This course has two midterms and a final exam. To study for these assessments, review tutorial problems and practice questions in addition to past exams. Once you understand how to think about problems in this course and have seen sample solutions, you’ll begin to adopt the right problem-solving mindset and develop intuition as to when you should apply certain linear algebra principles. Note that you won’t succeed in this course just by completing a few past exams due to the proof-based questions. You’ll need to practice regularly and truly attempt to digest all the content to build your proof-based mindset.

Find past MAT185 Exams on courses.skule.ca.

How to Succeed

Quick tips and equations

  • Understand the concept of vector spaces. As you’ll learn soon enough, vectors are more than just “pointy arrow thingies!” Know the proof for vector spaces by heart.

  • Know the difference between \bigcap and \bigcup , as well as \subseteq and \subset .

  • \text{rank}(\textbf{A}) = \text{dim}(\text{col}(\textbf{A})) = \text{dim}(\text{row}(\textbf{A}))
  • The rank-nullity theorem: \text{dim}(\text{null}(\textbf{A})) = n - \text{rank}(\textbf{A}) , where \textbf{A} is an m x n matrix with real values.  

  • \text{det}(\lambda\textbf{I} - \textbf{A}) = \textbf{0} : Characteristic equation of matrix \textbf{A}

More Details

MAT185 builds on concepts from ESC103, such as vectors and matrices, and requires you to use them for proofs instead of computations. Therefore, you should thoroughly understand all the content from ESC103; concepts in MAT185 are VERY connected, so a shaky foundation will make your semester more difficult.
As mentioned earlier, practice is necessary for success in MAT185. Solving a variety of problems will help you learn different problem-solving methods. You’ll become more comfortable with proofs and will build your linear algebra intuition – both critical in this course.

Sometimes, it’s difficult to even start a linear algebra problem. Don’t cave and look at an answer key right away: this practice will hurt you in the long run. If you don’t know how to start a problem, write down what you know about it, such as relevant equations, facts, and theorems. Once these tools are laid out in front of you, it’ll be easier to connect the dots and develop a solution.
Even if you think you know how to solve a problem, ensure that you can solve it with a formal and rigorous proof! That being said, don’t waste your time creating a sophisticated proof for every single easy question.

In this course, your main job is connecting different facts and theorems to prove and disprove statements. Physically organizing and writing down theorems and equations will help you get organized in your head and understand how they connect.

Linear algebra is not a new subject. If you have trouble understanding a concept, there are a lot of online resources through which you can gain intuition and look for different perspectives. These different interpretations are what make linear algebra great. Sometimes a physical, geometric interpretation makes the most sense. Other times, equations will just congregate together in your head. Experiment and find out what’s best for you.

Beyond First Year

  • This course will give you lots of problem-solving experience. Linear algebra is an abstract and general topic in math; there are often many ways to approach a problem, and you’ll get to experiment with this. 

  • Linear algebra has applications all over engineering and science. For example, most circuit problems are solved using matrices. Quantum mechanics make use of special matrices to determine what’s possible for a particle. In computer science, vectors can be used in gaming and graphics. Google uses eigenvectors to determine the ranking of pages in a search. Linear algebra is a necessary tool for robotics, machine learning, and for any field you’re interested in. 

  • Many of your upper-year courses will require strong knowledge and frequent use of linear algebra