Should I retake Real Analysis I?

[Josep]

Hi all,

I am currently in my first semester of my sophomore year, taking Real Analysis I. This class covers formal proofs, properties of the real line, sequences, series, limits, continuity and differentiation, and Riemann Integration. I apparently got stuck with the worst professor at my university to take the class with (according to my senior friends majoring in mathematics as well).

My problem at the moment is that I am probably going to get a C in the class. In class, he writes the definitions on the chalkboard, then he writes the theorems, and proves them, changing a symbol or letter here or there to make it different from the book, which I think is not an effective teaching method. The professor has a history of having low averages on his midterms and quizzes. On our 1st midterm, the class average was a 42/100. I had scored a 74/100. The test was later curved to be out of 80. On our first quiz, I did rather poorly and got a 21/40, which was also the class average. I went to his office hours to ask him for advice on how I could better study, I took his advice, and on the next midterm, which I had thought I did well on, I scored a 62/100. The class average was a 50/100. This test was not curved. There were 31 students at the beginning of the semester, and now there are 21 students.

I am a double major in Computer Science and Mathematics, and in the past I had done very well. When I took Multivariable Calculus my 1st semester of freshman year, I received an A, and I was usually the top scorer on many exams. The same happened with Differential Equations and Linear Algebra my 2nd semester of my freshman year, except in Linear Algebra, my "top scores" were much lower. I took the same professor that I have right now for Linear Algebra, and I received the highest score on the final, but that was an 84/100. I am pretty sure he curved the class or something, as I got an A in that as well.

My friend said I could just continue onto Real Analysis II since I will have a better professor "for sure" in that class, but I would like to gather more opinions. Right now, the only good professor for Real Analysis I next semester is already full, and I don't want to risk taking the class again with a bad professor. I could take Real Analysis I again next semester and risk getting a bad professor, or I could take Real Analysis II, then retake Real Analysis I to get a better grade (and hopefully take it with a better professor), or I could take the C in the class and not retake it. I am just worried that I will fall behind in my Mathematics major, or that if I don't retake the class, employers for internships will see my C and my GPA might look bad. I would talk to my Mathematics advisor, but he is the same person as my professor.

Oh, and sorry for the long post. I know some people like as many details as possible when trying to answer a question, so I've tried to include as much as I could.

 

[FactChecker]

I think that two important questions to ask yourself are:
1) Do you understand the material well enough to continue?
2) Is there a way that you can rely more on a textbook and less on the instructor?

 

[Josep]

I think that two important questions to ask yourself are:
1) Do you understand the material well enough to continue?
2) Is there a way that you can rely more on a textbook and less on the instructor?

1) I understand the theorems and definitions well enough to continue. I would say that when it comes to doing the actual proofs, I am okay at them.

2) I would like a good book to use, but I don't really know of any good textbooks. For the textbook I have, when I finish my work, I would like to check over it, but I never can because the book doesn't provide you solutions.

 

[Meir Achuz]

If you don't like or do well in real analysis, you should consider a major other than mathematics.
I became a theoretical physicist.

 

[Josep]

If you don't like or do well in real analysis, you should consider a major other than mathematics.
I became a theoretical physicist.

I completely forgot I had this account. I decided to continue and am doing my PhD now, focusing on a specific area in number theory.

 

[FactChecker]

I completely forgot I had this account. I decided to continue and am doing my PhD now, focusing on a specific area in number theory.

Very good! So you are the best person to answer the question of your prior self. What advice would you give him now?

 

[Josep]

Very good! So you are the best person to answer the question of your prior self. What advice would you give him now?

Thank you!

The first thing I did was dedicate more time to practicing proofs and questions from my textbook. I was practicing questions already, but I decided to set a goal for how many problems I wanted to solve for a topic based on how uncomfortable I was with it by a specific date.

The second thing I did was go to alternative sources for help other than my professor. Looking back, it was definitely true that my professor wasn't good, but there were other sources of help. If I had questions about any topic that interested me, there was something I didn't understand, needed help solving a problem, or wanted my proofs reviewed, I would either go to the math building's math lounge or post online.

Lastly, once I got into harder classes, I began helping people a lot more, which I think solidifed my understanding. These harder classes brought along harder problems and so there were less people to ask for help. Classmates and I would sometimes get together and try to tackle specific problems that were giving us all trouble. I think collaborating with others helped introduce me to how others might think about solving a problem rather than just how I might solve it.

 

[FactChecker]

Thank you!

The first thing I did was dedicate more time to practicing proofs and questions from my textbook. I was practicing questions already, but I decided to set a goal for how many problems I wanted to solve for a topic based on how uncomfortable I was with it by a specific date.

The second thing I did was go to alternative sources for help other than my professor. Looking back, it was definitely true that my professor wasn't good, but there were other sources of help. If I had questions about any topic that interested me, there was something I didn't understand, needed help solving a problem, or wanted my proofs reviewed, I would either go to the math building's math lounge or post online.

Lastly, once I got into harder classes, I began helping people a lot more, which I think solidifed my understanding. These harder classes brought along harder problems and so there were less people to ask for help. Classmates and I would sometimes get together and try to tackle specific problems that were giving us all trouble. I think collaborating with others helped introduce me to how others might think about solving a problem rather than just how I might solve it.

These suggestions sound like great advice! Thanks.

 

[mathwonk]

As a professor many students considered "bad" myself, I read this with interest. The only bad quality you mentioned about your professor, other than his choice of notation, was that his standards were higher than you were used to. Of course he may have been poor at explaining as well. But low average scores do not necessarily mean a professor cannot teach well. And the higher standards he exposed you to may have helped you. In your very lucid and intelligent recap of what changed in your experience, i.e. from doing so - so or better, to doing well, you describe qualities such as learning to collaborate, that suggest the main difference was that you yourself became a better student. Congratulations!

A famous experiment at Berkeley, carried out by Uri Treisman, showed that young college students who had been honors students in high school, but possibly at somewhat weak schools, arrived at Berkeley not realizing the great jump in standards, and the necessity to strengthen their study skills, e.g doing harder problems, collaborating with others. When taught these skills, students who had been struggling, even failing, became honors students. You seem to have discovered these very things on your own.

I was a victim of this syndrome myself, going from literally high school state champ in math in my little southern state, to getting D's in math in an elite college. But I persisted and eventually became a PhD in algebraic geometry after a long struggle. You have done better quicker than I did, and I have every confidence you will have a fine career. Congratulations again, and best wishes.