Author: orientation

ESC102: Praxis II

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Praxis II is a continuation of Praxis I. In this course, you will apply the processes and concepts you learned in the fall to improve the lived experience of a community in the Greater Toronto Area (GTA). Even more so than Praxis I, Praxis II is all about teamwork. You will be divided into teams in the third week, and the rest of Praxis II will be based on team activities. 

Your first team project is to construct a community profile where you meet with and analyze a specific community’s baseline conditions and trends. After that comes the true heart of Praxis II. After identifying an engineering opportunity based around a specific community, you will create a Request for Proposal (RFP), which is like the design brief from Praxis I except far more detailed. The teaching team will then select around 8-10 RFPs to share with the entire class, and your team will choose one of these RFPs and develop a solution for it. 

People are attending the Praxis showcase event in a hall with wooden vaulted ceilings, viewing posters and engaging in conversations. Tables with displays and informational materials are set up around the room.
Previous years’ students present their designs to professors and public attendees during the Praxis II Showcase at Hart House

Next, you’ll prototype, test, and document your solution. The difference from Praxis I is that now, the possibilities are far more open-ended. Your concepts can range from physical products to software to something else altogether. Most importantly, you are expected to make much more informed design decisions and perform much more rigorous verification. You’ll also get to take your solution to stakeholders in your community and ask them for feedback. At the end of the course, you’ll present and defend your chosen solution to the teaching team at a public event called “Showcase.” You can view previous Praxis II design projects on the Praxis II Showcase website. 

Professors

Professor Roger Carrick

Professor Roger Carrick

Professor Jennifer Lofgreen

Professor Jennifer Lofgreen

The instructors for Praxis II are Professor Jennifer Lofgreen and Professor Roger Carrick, whom you will recognize from ESC101 Praxis I. 

Course Highlights

  • Cold-calling businesses, companies, and communities. It can be awkward at first, but you’ll quickly become a pro and discover that it isn’t all that difficult. This is a super useful skill that you can use for job searching and networking later too. 

  • Praxis II encourages you to explore Toronto! You will go out into the GTA, meet new people, and learn new perspectives. You’ll be pushed out of your comfort zone in a good way. 

  • Prototyping and testing your solutions. Not only will you learn CAD software called OnShape, but your design concepts can also be literally anything you want – if you can support all your design decisions with research and verification. 

  • Praxis II Showcase! Local media have sometimes attended and featured students in their newspaper or on the radio. It is extremely fun to present and observe other teams doing the same. 

Week in the Life of a Praxis II Student

Like in Praxis I, the weeks in Praxis II can vary significantly. Here is a rough approximation of how a week will look for a Praxis II student. 

Lectures

Much of Praxis II is very similar to Praxis I, such as three lectures a week, as well as learning additional engineering design concepts. Just like Praxis I, lectures are still well-integrated with the tutorials (also known as studios). 

Tutorials (Studios)

Praxis II tutorials (studios) are very similar to those in Praxis I. They still take place smaller groups, are led by teaching assistants, and are where most of your team-based project-specific work take place. 

Practicals

The two-hour practical blocks work the same way as they did in Praxis I. Once again, it is simply a suggested meeting time, and you may choose to meet as much or as little as your team deems necessary on a weekly basis.

We cannot emphasize enough the importance of regularly checking in with your team. Make sure that everyone is regularly contributing and do not leave work until the last minute. Note that the workload in Praxis II significantly increases from Praxis I, so be prepared for a lot of teamwork. Through regular team communication, you can keep track of deadlines and allocate work more effectively. Communicating with your team helps ensure that everyone is healthy and offers an opportunity to organize hangouts together to relax. Speaking from experience, it is worth the time and effort to organize group activities to have fun and build team spirit. 

Individual Assessments

In place of a final exam, there is a final independent deliverable in Praxis II: the Student Engineer Portfolio.  

The portfolio is a chance for you to reflect upon your engineering design work throughout first year and understand how your positionality affected/was affected by your design work. Furthermore, it offers you an opportunity to flex your engineering muscles and describe your skills and abilities which went into these projects. We were asked to talk about our engineering design process in Praxis I, CIV102 Bridge Project, as well as Praxis II, so make sure that you have been recording and organizing evidence of what you did during these projects. Note that many companies allow prospective engineers to submit a design portfolio to display some of their work, so this assignment can be an asset in the future. 

In the past year, the portfolio was due a few days after showcase. It is a good idea to work on the portfolio throughout the semester, potentially throughout the year. Taking 5 or 10 minutes every so often throughout the year to record some notes about your design process and the concepts, tools, models and frameworks (CTMF) that you’ve used in Praxis I, CIV102 Bridge Project, and Praxis II will ease a significant portion of your burden when it comes time to submit the portfolio. Trust us when we say you will want to spend as much time preparing for your other final exams instead of working on your portfolio. 

Group Assessments 

You will spend most of your time in Praxis II working in one group. You will write the community profile, RFP, and complete the Showcase project in this group. However, there will be some individual assignments. In addition to the handbook and portfolio, your first two assignments, the community profile and positionality statement, will be independent. 

How to Succeed

Nearly all the tools you used in Praxis I will be used in Praxis II. We have listed some more tools specific to Praxis II below.

More Details

Your team can get caught up in small details; though discussion and debate are at the heart of Praxis, ask yourself if your team’s decision will affect your design’s use and function or your ability to defend your design. If there is little impact, aim to conclude the debate by picking one of the possible options. If done correctly, it’s fine to say, “This part of the design was not significant, so we simply picked one option.”

Planning is crucial in Praxis II: there’s a lot to do and there’s limited time. Being a skilled planner will help you immensely in the course.

You should have a high-level plan before you begin working. At the beginning of each task, quickly summarize what you want to achieve and your plan to achieve it. This is especially useful when justifying your design. If you plan your argument step-by-step, you’ll have a much easier time writing clearly and concisely.

However, don’t over plan! Sometimes a detailed plan is unnecessary since you know what you’re doing. Conversely, if you’ve never done the task before, you won’t know what to include in your plan. In these cases, try to work a little first to get an idea of how long something takes or the type of work it requires – then make your plan.

In high school, you may have been used to your teacher ignoring or going easy on any obvious mistakes or weaknesses in your project if the rest of it was good. In Praxis II, the markers’ job is to be critical of your design and design process, so if there’s a clear weakness, they will ask you to address it. Thus, it’s your job to have a well-rounded design that you can fully support. If your team seems to be ignoring something about your design, bring their attention to it. Think about situations in which the design can fail and then build some arguments for why those situations are unlikely. A little self-criticism goes a long way in Praxis!

Praxis II is a course that really benefits from your engagement and enjoyment of the work. Since you have a lot of choices in picking your engineering opportunity, look for communities and situations that you’re personally interested in and care about. Having a genuine interest in your work will help you in lots of ways, especially by motivating you to do the little extra research or experimentation that can turn your design from good to great.

You will be working with the same team for four months, so get to know them. What do they like? What do they dislike? Do they have pets? Why are they late every day? Did they commute in the morning? What do they want to get out of this team? What are your team goals? The key to individual success in Praxis is to be successful as a team.

Praxis II is one of the most unique and engaging courses you will take during your first year in Engineering Science. The amount of trust and responsibility given to students is almost unparalleled. Enjoy your time in Praxis II and try to get the most out of it! You could learn skills that you use throughout your life.

What Will You Take Out of It?

  • Like Praxis I, Praxis II gives you the opportunity to turn your personal interests into engineering opportunities. You will have the opportunity to do what you excel at or to learn something brand new! 

  • You will get the opportunity to build on and apply the Engineering Design principles taught in Praxis I, including the FDCR principle and Toulmin model of arguments. 

  • In Praxis II, there’s more time to spend on prototyping and testing. Use the course as an opportunity to pick up some hardware or software skills. 

  • You’ll be designing a solution for an opportunity to support a community. This is a great way to learn about the human components of engineering, like communicating with your stakeholders, accounting for accessibility, and verifying your design. 

  • The design skills gained in this course will serve as a basis for second-year EngSci courses such as ESC204 as well as upper-year design courses in almost all of the majors. 

Praxis Showcase in the News

Media have attended some of the Praxis Showcase events. The stories in the links below detail some of the past student projects. 

Praxis Showcase 2019 Featured in U of T News
Praxis Showcase 2018 Featured in The Star

ECE159: Fundamentals of Electric Circuits

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When people find out I’m not very good at building circuits, they’re shocked! 

Circuits are the building blocks of all electrical devices – including the device on which you’re reading this right now. In EngSci’s introductory circuits course, ECE159, you’ll be introduced to circuit properties such as current, voltage, and resistance, as well as circuit components like sources, resistors, capacitors, inductors, and op-amps. You will learn about DC (direct current) and AC (alternating current) circuits, and will use techniques like mesh analysis, nodal analysis, Thévenin equivalents, differential equations, and complex numbers to analyze circuits. 

The goal of the course is to solve circuits for their properties by understanding how their components interact. These interactions are expressed mathematically, so a large portion of this course is solving systems of equations. Succeeding in the course requires understanding the theory behind circuit analysis, being able to build circuits in real life and, most importantly, knowing how to apply the right formulas in the right situations. Are you ready to learn the fundamentals of harnessing electricity? 

From Israel Palacio on [Source]

Practice and regular review will be your best friend in this course. The key is to practice the steps to answer every type of question, as there are only a handful of distinct questions that can be asked on a test. Also, although electricity can be more difficult to comprehend than larger, mechanical systems, try your best to develop intuition for the concepts in a way that works for you. 

Professor

Portrait of Professor Tate
Professor Tate [Source]

Professor Zeb Tate

Professor Joseph Euzebe (Zeb) Tate is an Associate Professor in the Department of Electrical and Computer Engineering. He completed his BS in electrical engineering from Louisiana Tech University and received his MS and PhD from the University of Illinois. He joined the University of Toronto’s ECE department in 2008 as an assistant professor. Professor Tate’s research focuses on improving the reliability and efficiency of power grids through combining advanced telemetry and data processing.

Professor Interview

“I think mainly empathy is a really big piece of [my teaching philosophy], trying to put yourself in the shoes of someone that doesn’t know the material […] so I really try and question the assumptions that I’m making when I go into a classroom as to what the students know in advance and try and make sure nobody gets left behind by those kind of poor assumptions.” 

“The circuit analysis techniques we use […] appear frequently. Sometimes very explicitly—they’ll say, “We’re going to model this chemical process as if it were a circuit,” and then solve it that way. […] There’s also a lot of benefit in the actual circuit analysis—the specific techniques. Specifically, using matrices is a really powerful way of solving things, and it’s not just electrical engineers who use it. Civil engineers, for example, also apply it.” 

“I would say, reach out […] for help if you think you might need it at all. There’s no downside to contacting your professors early on. […] First, it builds a relationship, which can be helpful if you ever need a reference letter. And second, there’s no substitute for one-on-one instruction when it’s really what’s needed.” 

Course Highlights

  • Labs. Every other week you’ll have the chance to create circuits on breadboards. Be ready not only to build circuits but to have fun. 

  • Have you ever looked at a circuit diagram and thought, “I wish I knew what this all meant”? Well, you will be able to interpret and analyze many different types of circuits after ECE159! 

  • This course will introduce you to using complex numbers to model real systems.  

Week in the Life of an ECE159 Student

Lectures

There are typically three hours of ECE159 lectures a week. Be sure to pay attention during these lectures: this is where you learn about the circuit laws you’ll use to solve problems on assignments. In lectures, the professor will conceptually explain circuit topics, as well as go through many examples of circuit analysis. Note these examples down, as they serve as models for midterm and exam questions.

Tutorials

There is one hour of ECE159 tutorials built into your weekly schedule. During the tutorial, the theory of the course will be briefly summarized. However, the emphasis during the tutorials is on learning how to problem-solve. Your TA will work through lots of different examples, and we recommend taking notes of their problem-solving steps. ECE159 TAs are extremely helpful, so make sure to pay attention! 

Practicals (Labs)

ECE159 labs are held every other week. Make sure to do the pre-labs before every lab session, as they’re worth marks but are also crucial to your ability to understand the lab. They can be a time crunch because the whole lab is done in a three-hour period. During this time, you’ll build circuits in the lab and observe their properties with different electrical instruments such as oscilloscopes. 

Labs (Practicals)

Your performance during labs will be graded, so take them seriously. Although three hours may seem like a lot of time, the labs are relatively long, and many students do not end up finishing some labs on time. TAs will grade the notes you take during labs, your ability to build circuits, and your respect for the workspace. 

Midterm and Exam

ECE159 has a midterm and a final exam. They consist of circuit analysis questions, and each question can be thought of as multiple difficult questions packed into one. For both exams, you will be permitted to bring a single double-sided handwritten aid sheet. 

How to Succeed

Quick tips and equations

  • Passive Sign Convention: if positive current flows out of the positive terminal of a voltage source, then the element is delivering power. Otherwise, it is absorbing power. 

  • Consider the hydraulic analogy, where voltage and current are analogous to water pressure and flow of water, respectively. 

  • V = IR (Ohm’s Law)

  • P = VI (Electric Power)

  • These are general equations to represent voltage and current in a circuit:
    • v(t) = v(\infty) + [v(0) - v(\infty)]e^{-t/\tau} or
    • i(t) = i(\infty) + [i(0) - i(\infty)]e^{-t/\tau} 
Common electric circuit component diagrams
  • You’ll learn how to use complex numbers to model AC circuits. Normally, this would involve many difficult computations. However, certain types of Faculty-approved calculators can perform almost any complex calculation for you. 

  • Remember that circuit analysis is a mere representation of the physical world; if during a lab your data is not exactly as you had expected, don’t worry. Small sources of error are common. 

More Details

This course may start off looking like basic high school review. However, it kicks into gear later, so make sure not to fall behind so that you aren’t caught off-guard. New topics will start to be introduced very quickly, and they will build upon all the old techniques and material that you’ve been learning throughout the course.

Technically speaking, you could get through this course just by knowing nodal and mesh analysis. However, you’ll waste considerable time on questions if they’re all that you use. Pay attention to concepts that can speed up your problem solving. Examples include the fact that parallel branches have the same voltage or that certain op-amp configurations are designed to perform addition, subtraction, differentiation, and integration.

The best way to remember the equations and how they connect is by writing an equation sheet as the course moves on. This will also be a helpful resource when you work through homework problem sets – and on the exams, you will be allowed a single double-sided handwritten aid sheet.

This course is about problem-solving, which means the more questions you practice, the more you’ll succeed. The lectures are also designed to be interactive and will focus on working through lots of examples. Find past ECE159 midterms and exams on courses.skule.ca.

Like classical mechanics, which you’ll learn in PHY180, introductory circuits is a very old and standard course. There are many online videos and textbooks that you can use if you’re struggling with a concept and need a new perspective.

Beyond First Year

  • You’ll get crucial experience in building circuits, which is important in engineering prototyping (you will likely need this in Praxis III, in your second year, and you can use these skills on design teams and for personal projects). 

  • This course will provide a foundation for all upper-year electrical engineering courses and the coursework for majors such as ECE and Robotics. 

  • Even if you don’t find electronics interesting, the problem-solving skills you develop in this course will be used heavily in future courses with many connected concepts and equations, such as thermodynamics. 

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 is 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 loosely a 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 is 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: it’s time to learn! 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 is little correlation between how you felt about ESC103 and how you will feel about MAT185. Although 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 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 transferring to the University of Toronto as a professor, he taught advanced manufacturing and mechatronics as an assistant professor at the University of Kent, UK.

Instructor Rhupert Ashmore-Sharpe
Instructor Rhupert Ashmore-Sharpe

Instructor Rhupert Ashmore-Sharpe

Rhupert grew up in the heart of Toronto, and completed his bachelor’s and master’s degrees at UofT in Mathematics. He is currently working towards a PhD in numerical analysis and scientific computing. He has been a TA for over 5 years, teaching multiple first and second year courses in calculus, linear algebra, and complex analysis. More recently, he was an instructor and coordinator for the summer session of Calculus with Proofs (MAT137). In his spare time Rhupert enjoys playing piano, biking around town, and thinking about game design. 

Professor Interview

“I have an idea that you can’t prove something that you don’t believe in already. So I like to take time before I launch into a proof or a topic to talk about why we should think it’s true.”

“Thinking about something as simple as linear transformations but then seeing what you can do with them [through] fancy animations where you can really change a space and compress it or stretch it or compress it […] It really opens your view to computer graphics or physics and everywhere where linear algebra is used.”

“I always think about learning linear algebra like learning a programming language. If you learn a programming language, you need to know all the key words, so those are all your theorems and tools [in linear algebra], and then your using those key words or your tools in your proofs.”

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 are 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, and you are 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. 

Before every lecture, you’ll have to complete a textbook reading along with an online quiz. Ensure that you do these, as they’re crucial to understanding the concepts that will be covered more in-depth during the lecture (they are also worth marks). 

Tutorials

There is 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. 

Problem Sets

Approximately every month there is a problem set, with the option to work in pairs. You’re usually asked to prove or disprove some statements. The problems are relatively difficult, but you get a week to think about them and work on a solution. Try your best and these problem sets will be valuable practice. The problem set contents are similar to the more difficult exam questions.  

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. 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 upon 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 problem in Linear Algebra. Don’t cave in 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 do think that 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 is 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 usage of linear algebra/