Preparation Material for Analysis I

[NATURE.M]

Hi, I will be enrolling in an Analysis I course (highly theoretical calculus course, emphasizes proofs) at UofT this upcoming fall and was wondering if there are any materials that can adequately prepare me for this course.

 

[X89codered89X]

I'm interested in this as well. I'm aware that the standard text on the subject (often considered the gold standard) is Rudin's Real and Complex Analysis. It's referenced all over the place. Chances are your analysis course is at no more sophisticated of a level than this.

 

[zapz]

For an Undergrad Analysis I class, chances are you'd use Rudin's Principles of Mathematical Analysis, not Real and Complex Analysis which is usually graduate level as far as I know.
As for preparation, I suggest reading through the book beforehand, as well as working out sketches of the proofs for the main idea. Also, get feedback on your proofs so you know what's wrong and why, instead of the grading simply taking off a point.

 

[NATURE.M]

For an Undergrad Analysis I class, chances are you'd use Rudin's Principles of Mathematical Analysis, not Real and Complex Analysis which is usually graduate level as far as I know.
As for preparation, I suggest reading through the book beforehand, as well as working out sketches of the proofs for the main idea. Also, get feedback on your proofs so you know what's wrong and why, instead of the grading simply taking off a point.

Okay, I realized I didn't mention earlier that its a first-year course. Do you know of any online resources that deal with similar concepts, as I'd prefer to purchase the actually textbook later (probably in June/July).

 

[zapz]

http://ramanujan.math.trinity.edu/wtrench/texts/TRENCH_REAL_ANALYSIS.PDF

I think this is a pretty solid resource, and offers some different proofs from Rudin and co

 

[NATURE.M]

http://ramanujan.math.trinity.edu/wtrench/texts/TRENCH_REAL_ANALYSIS.PDF

I think this is a pretty solid resource, and offers some different proofs from Rudin and co

Thanks a lot, this will be very helpful :)

 

[jasonRF]

Okay, I realized I didn't mention earlier that its a first-year course. Do you know of any online resources that deal with similar concepts, as I'd prefer to purchase the actually textbook later (probably in June/July).

Do you mean this is a course for freshmen undergrads? Perhaps an honors calculus sequence?

 

[Robert1986]

I think that Spivak's Calculus book would be a good prep. This book is kind of a stepping stone from a "normal" calculus class to an analysis class. I doubt you will be using Real and Complex Analysis as this is a graduate level text and without having undergrad analysis, this book will be very difficult to get through. (It is already pretty hard to get through if you are familiar with analysis.) You might be using Rudin's Mathematical Analysis, which is meant for undergrads (this is called "Baby Rudin".)

 

[NATURE.M]

I think that Spivak's Calculus book would be a good prep. This book is kind of a stepping stone from a "normal" calculus class to an analysis class. I doubt you will be using Real and Complex Analysis as this is a graduate level text and without having undergrad analysis, this book will be very difficult to get through. (It is already pretty hard to get through if you are familiar with analysis.) You might be using Rudin's Mathematical Analysis, which is meant for undergrads (this is called "Baby Rudin".)

Yeah its a first year undergraduate course. I actually think the Spivak's Calculus book is the required text, but not 100% sure. I'm not sure if you would know, but is the link to the text provided above, material that I would probably study for the first year course.

(http://ramanujan.math.trinity.edu/wtrench/texts/TRENCH_REAL_ANALYSIS.PDF)

 

[NATURE.M]

Do you mean this is a course for freshmen undergrads? Perhaps an honors calculus sequence?

Yeah its a freshman college course.

 

[Robert1986]

Yeah its a first year undergraduate course. I actually think the Spivak's Calculus book is the required text, but not 100% sure. I'm not sure if you would know, but is the link to the text provided above, material that I would probably study for the first year course.

(http://ramanujan.math.trinity.edu/wtrench/texts/TRENCH_REAL_ANALYSIS.PDF)

That link looks more like an Advanced Calculus class and it is probably more along the lines of what is in Spivak rather than what is in a "true" analysis course. If the Table of Contents is a good indication, the link has a few topic not covered in Spivak (the multivariable stuff.)

I would say that right now, what you need is pretty good grasp of calculus. Really, if you know how to differentiate something how to find the integral of something, and what each means, then you are probably ready for the class you will be taking (assuming Spivak is the text you will be using.) You also need to be comfortable with stuff covered in a typical high school algebra class (that is, a typical high school algebra class in the US.)

 

[NATURE.M]

Alright thanks a lot.

 

[glueball8]

Spivak's Calculus is used. At least for 2-3 years before this year. Its is mainly proofs, there aren't much calculations except during tests for free marks. (We basically skipped over all calculations, like how to take integrals... If the integral is hard then its probably a even or odd function =/ or some trick.) Read over Spivak's over the summer would be very helpful, its probably the best math book you will use at UofT... Focus on proof methods like induction, contradiction, epsilon-delta.. There is a solution manual for Spivak's. Try not to get intimidated during the first few weeks of the class, the prof will usually go really fast and try to scare people into dropping. The pace will slow down after many people leave. =.= (We started off with 150+ people and ended with ~25.)

 

[NATURE.M]

Okay thanks, so you would advise studying integral calculus in depth this summer as well, since the notion isn't really discussed.
And in terms of difficultly (like dealing with proofs) will determination and hard work be enough to pull out >70%, in your opinion.

 

[glueball8]

Of course... you don't have to be a genius to well. Though if your aiming for a 70 then you might want to switch out because 257 is much much harder than 157. (Also, a lot depends on your Prof.) The course is actually not too bad, most people haven't done proofs and most people have a hard time with it. So it won't be only you, if you do have a hard time. But time management is very important since you have mat240 and physics courses to worry about too. I personally used all Sunday for Mat157.

You definitely need to learn all the material for AP math before the course starts. The Prof. assume you know all of that. I still recommend you read some Spivak, because AP math will not prepare you.

 

[NATURE.M]

The specific program that I'm interested in, is the specialist in mathematics and physics. And the program requires MAT157Y and eventually MAT257Y, and therefore I can't take a MAT137Y course. Nonetheless, I'm going to read through and try to work out some problems in spivak's calculus for preparation, as the specialist leaves my options open for both math and physics graduate programs.

 

[Arsenic&Lace]

I found that working through all of the theorems and their proofs was fairly essential to understanding the subject; in an elementary calculus course, you can get by with a brief overview of a proof (or a sketch of a proof even) and concentrate on applications, but genuinely understanding the proofs in question was essential for me in advanced calculus.

 

[glueball8]

The specific program that I'm interested in, is the specialist in mathematics and physics. And the program requires MAT157Y and eventually MAT257Y, and therefore I can't take a MAT137Y course. Nonetheless, I'm going to read through and try to work out some problems in spivak's calculus for preparation, as the specialist leaves my options open for both math and physics graduate programs.

I know. I'm saying that you need to do great in MAT157 to survive in MAT257. So if your aiming for a 70 in MAT157 then MAT257 will be a nightmare.

You will know if you like math or physics better by the end of 1st year, at least end of 2nd ear.

If you want to be prepared for the program, I suggest reading some of Linear Algebra (Friedberg, Insel, Spence) which WAS used for MAT240&247. Also, KNIGHT was used for physics, you should read some of that as well. Pick your bird courses carefully, make sure it is a bird course. Mat157+240+Phy151's work load is equivalent to most other programs. Math & Physics Sp. is known to be Canada's hardest program for a reason.

 

[NATURE.M]

Thanks again, and in terms of 'bird' courses, I was thinking about History/Philosophy of Science, Science/Values, Life on other worlds (in astronomy section), and maybe an intro to ethics course, as these will help me obtain the breadth requirements, and I also happen to have some interest in these topics. In your opinion do these courses seem like 'bird' courses?

 

[glueball8]

Um I don't really know what is a good bird course. I'm just saying you don't want to add much more workload. I took CompSci and eco100. Both weren't bird courses (I thought they were.) and end up having work overload. I think ethics courses are a 4th year requirement. (? you should check the calendar.)

You might want to ask around. But you shouldn't worry about those courses that much. I took eco100 as a bird course which was a mistake. (eco105 is actually the easier course, but higher up in number :S, normally uoft has lower number course as easier.) Eco100 was the hardest course for commerce students, so its definitely not a bird course, have less than 1/2 the workload of MAT157 though.

They changed the general requirements at uoft last year, I don't know what courses you need to take to fit the general requirements. I haven't taken any of the courses you mentioned, they seem like good "bird" courses. (There aren't any real bird courses in UofT though...)

 

[NATURE.M]

Um I don't really know what is a good bird course. I'm just saying you don't want to add much more workload. I took CompSci and eco100. Both weren't bird courses (I thought they were.) and end up having work overload. I think ethics courses are a 4th year requirement. (? you should check the calendar.)

You might want to ask around. But you shouldn't worry about those courses that much. I took eco100 as a bird course which was a mistake. (eco105 is actually the easier course, but higher up in number :S, normally uoft has lower number course as easier.) Eco100 was the hardest course for commerce students, so its definitely not a bird course, have less than 1/2 the workload of MAT157 though.

They changed the general requirements at uoft last year, I don't know what courses you need to take to fit the general requirements. I haven't taken any of the courses you mentioned, they seem like good "bird" courses. (There aren't any real bird courses in UofT though...)

Alright, anyways thanks again for the advice, its good to hear from a former u of t student (or current..).

 

[Sankaku]

For intro analysis, you can't do better than watch these:

Francis Su (Harvey Mudd College):
http://analysisyawp.blogspot.ca/
http://www.youtube.com/playlist?list=PL0E754696F72137EC

 

[PSarkar]

I am in the same specialist program at U of T (now going into 2nd year). MAT157 uses Calculus by Spivak. It's a really good book and I think Spivak does really well explaining everything in detail so there shouldn't be any problem studying it yourself. So might as well buy it right now and study from it. I saw your other post about linear algebra textbooks. For Mat240 and MAT247, the right textbook to use is Linear Algebra by Friedberg, Insel and Spence: https://www.amazon.com/dp/0130084514/?tag=pfamazon01-20 (unless they changed it for 2013/2014). If you have any other questions about the program feel free to message me.