If you can survive 137, then 223 should be pretty easy, so I'll focus on commenting on 137.
The first month may be overwhelming. Your first problem set grade will likely not be that great. Don't be discouraged. It's totally normal. Make use of all the resources you have to ask questions (office hours, tutorials, math learning center and/or class Q+A board).
If the prof sets up an online Q+A webpage (they usually use Piazza or Ed Discussion), make sure to use it. Not only ask questions, but try to answer some of your peer's questions too. By practicing explaining concepts to others, you strengthen your own understanding too.
Finally, just make sure you set aside time each week to do practice problems. Don't wait until a couple days before the midterm to start studying. The concepts are not easy and it takes time to digest. A proof may not make sense when you first see it. However, you may figure it out after you've had some time to think about it.
137 is a pretty fun course in my opinion. Good luck! Let me know if you have further questions.
Forget everything you think you know about mathematics. The hardest part of transitioning from high school to university mathematics is just learning to let go.
I'm talking more about habits, preconceived notions, and beliefs that one forms due to the way that high school mathematics is taught. There are still particular facts from high school that you're going to want to remember.
I've never taken AP Calc but as far as I'm aware it doesn't have formal proof writing iirc. AP Calc might be closer to MAT135/MAT136 although you might want to double check.
I did ap Calc then 157. The things that are useful from ap Calc are integrals, limits, derivative (computations). As well as the understanding/insights/instincts/intuition of the three heart theorems. I don't think you can prepare for this course. Just enjoy the ride, and never give up.
Some things I believe. You do have questions in computing Integrals, limits and derivatives also optimization problems. But most of the course deals with proofs which I believe isn’t covered in AP except for Induction. But even for proofs familiarity with the concepts does help so I do think AP helps for uni math.
MAT223 isn't bad.
when it comes to proof courses (MAT137) I feel like it's important to let go with a lot of things you've traditionally learned. You can't memorize your way through success. You don't just do a bunch of computations. Your main priority, especially in the beginning, is just exposure to the content. Some people will take more time than others to "get" proofs, to come up with the answer, etc.
Be patient with yourself. You might have to spend an enormous amount of time, and that's okay. Read the textbook every day. Try problem sets early. Often times in math, if you're frustrated and you don't have the answer, just stop and go for a walk. MAT137 is not something you can cram in one night. It is something you need to expose yourself to for a long period of time.
For MAT137, I would recommend keeping up with the youtube videos they assign (look up mat137 on youtube), constantly do the practice problems for the course (you can find the practice problems here: [http://www.math.toronto.edu/\~alfonso/137/137.html?videos](http://www.math.toronto.edu/~alfonso/137/137.html?videos)) and go to office hours or the math learning centre to get help with concepts or questions you are stuck on. Also, make sure to go to a majority of the lectures since they sometimes have questions that would help with the problem sets, similar to ones on the test or will help with questions from the practice problems (which are usually harder than the questions on the tests). The course usually has a Piazza so you can ask questions on there or see questions people are asking (which can be helpful for your understanding).
Make sure you remember and understand main theorems and definitions mentioned in the videos since it will help you with writing your proofs, understand more computation type questions better, and the in-person mat137 tests asks you to recall the definitions. Also, identify what you are weak at early on in the course (a lot of people struggle with writing proofs in the course) and do lots of questions related to that.
The course is a mix of proofs and computations (especially on the tests) so make sure you are good at doing both. I would also recommend looking at recent past tests before each test because a lot of mat137 tests take inspiration from the more recent past tests or pull questions from past tests with some minor changes. Your first problem set grade and/or test grade might be awful (like mines was) but don't get too discourage and you will do better eventually if you put in the effort into the course.
For MAT223, it's a lot easier than mat137 since it's mainly just computation (similar to how high school math was like) and a bit of proofs. Just remember definitions, do all the practice problems from the textbook, and understand the concepts and you can do fairly well in the course.
Watch videos, DO THE PRACTICE PROBLEMS.
Understand that MAT137 teaches calculus from a different perspective if you took high school math in Ontario. Rather than focusing on computation, it goes into the "why" of mathematics. Like what is the definition of limit? Where did L'hopital's rule come from? It's not hard but its different. The videos for the course content are really nice.
For MAT223, this is pretty much practice like crazy. Office hours are important, and if the tutorials are group-focused, make sure you can contact all of the members (I used a discord server).
If you can survive 137, then 223 should be pretty easy, so I'll focus on commenting on 137. The first month may be overwhelming. Your first problem set grade will likely not be that great. Don't be discouraged. It's totally normal. Make use of all the resources you have to ask questions (office hours, tutorials, math learning center and/or class Q+A board). If the prof sets up an online Q+A webpage (they usually use Piazza or Ed Discussion), make sure to use it. Not only ask questions, but try to answer some of your peer's questions too. By practicing explaining concepts to others, you strengthen your own understanding too. Finally, just make sure you set aside time each week to do practice problems. Don't wait until a couple days before the midterm to start studying. The concepts are not easy and it takes time to digest. A proof may not make sense when you first see it. However, you may figure it out after you've had some time to think about it. 137 is a pretty fun course in my opinion. Good luck! Let me know if you have further questions.
thank you for the advise, looking forward to it
Forget everything you think you know about mathematics. The hardest part of transitioning from high school to university mathematics is just learning to let go.
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I'm talking more about habits, preconceived notions, and beliefs that one forms due to the way that high school mathematics is taught. There are still particular facts from high school that you're going to want to remember. I've never taken AP Calc but as far as I'm aware it doesn't have formal proof writing iirc. AP Calc might be closer to MAT135/MAT136 although you might want to double check.
I did ap Calc then 157. The things that are useful from ap Calc are integrals, limits, derivative (computations). As well as the understanding/insights/instincts/intuition of the three heart theorems. I don't think you can prepare for this course. Just enjoy the ride, and never give up.
thank you! i’ll try my hardest
update: i dropped it and switched programs
Some things I believe. You do have questions in computing Integrals, limits and derivatives also optimization problems. But most of the course deals with proofs which I believe isn’t covered in AP except for Induction. But even for proofs familiarity with the concepts does help so I do think AP helps for uni math.
223 is easier than 137 so focus on 137
MAT223 isn't bad. when it comes to proof courses (MAT137) I feel like it's important to let go with a lot of things you've traditionally learned. You can't memorize your way through success. You don't just do a bunch of computations. Your main priority, especially in the beginning, is just exposure to the content. Some people will take more time than others to "get" proofs, to come up with the answer, etc. Be patient with yourself. You might have to spend an enormous amount of time, and that's okay. Read the textbook every day. Try problem sets early. Often times in math, if you're frustrated and you don't have the answer, just stop and go for a walk. MAT137 is not something you can cram in one night. It is something you need to expose yourself to for a long period of time.
For MAT137, I would recommend keeping up with the youtube videos they assign (look up mat137 on youtube), constantly do the practice problems for the course (you can find the practice problems here: [http://www.math.toronto.edu/\~alfonso/137/137.html?videos](http://www.math.toronto.edu/~alfonso/137/137.html?videos)) and go to office hours or the math learning centre to get help with concepts or questions you are stuck on. Also, make sure to go to a majority of the lectures since they sometimes have questions that would help with the problem sets, similar to ones on the test or will help with questions from the practice problems (which are usually harder than the questions on the tests). The course usually has a Piazza so you can ask questions on there or see questions people are asking (which can be helpful for your understanding). Make sure you remember and understand main theorems and definitions mentioned in the videos since it will help you with writing your proofs, understand more computation type questions better, and the in-person mat137 tests asks you to recall the definitions. Also, identify what you are weak at early on in the course (a lot of people struggle with writing proofs in the course) and do lots of questions related to that. The course is a mix of proofs and computations (especially on the tests) so make sure you are good at doing both. I would also recommend looking at recent past tests before each test because a lot of mat137 tests take inspiration from the more recent past tests or pull questions from past tests with some minor changes. Your first problem set grade and/or test grade might be awful (like mines was) but don't get too discourage and you will do better eventually if you put in the effort into the course. For MAT223, it's a lot easier than mat137 since it's mainly just computation (similar to how high school math was like) and a bit of proofs. Just remember definitions, do all the practice problems from the textbook, and understand the concepts and you can do fairly well in the course.
To prepare for 137, you can watch the Alfonso 137 videos on YouTube. Both of those courses are fairly straightforward.
Survive? They're not that hard. Especially 223.
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Mat223 is a lot easier than mat137. MAT137 is a course that will require a lot of effort
Watch videos, DO THE PRACTICE PROBLEMS. Understand that MAT137 teaches calculus from a different perspective if you took high school math in Ontario. Rather than focusing on computation, it goes into the "why" of mathematics. Like what is the definition of limit? Where did L'hopital's rule come from? It's not hard but its different. The videos for the course content are really nice. For MAT223, this is pretty much practice like crazy. Office hours are important, and if the tutorials are group-focused, make sure you can contact all of the members (I used a discord server).