Programs What Are Typical Exam Scores for Math Majors?

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Concerns about performance in an honors multivariable calculus and linear algebra course are prevalent among mathematics majors, especially after receiving an 81 on a recent midterm. The student expressed anxiety over a low score on a proof and questioned whether this indicated future struggles. Responses highlight that an 81 is a solid score in a challenging course, and it's common for students to face difficulties with proofs. Peers suggest focusing on understanding mistakes and improving proof-writing skills through practice, including studying advanced texts like Rudin. The discussion emphasizes that grades can vary widely among students, and a typical range of scores exists. Personal anecdotes illustrate that many students experience initial setbacks but ultimately succeed by persevering and seeking help when needed. Overall, the consensus is to prioritize learning over grades and to continue pursuing mathematics despite challenges.
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I'm currently a mathematics major taking an honors multivariable calculus/linear algebra course. My most recent midterm covering differentiability of multivariable functions, derivatives of matrix functions, chain rule, etc. was an 81. Granted, 4 points were lost only due to a simple calculation error (some more were lost by not rigorously proving a function was continuous at a point). I'm worried due to the fact that my proof on the exam (f:R^n->R^m, prove if f is differentiable at a, it is continuous at a) received a 10/20. Is this exam indicative of troubles ahead? Is it normal for math majors to receive scores like 81/100 on exams like these? I'm worried that I may not have what it takes because of this.

What are some of your experiences with grades? How did it affect your education in mathematics?

Thanks
 
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In an honors math class, I'd think a B would be pretty nice...

Check out how the other kids are doing. If everyone else aced the test with 95-100%, I would be worried, but it's much more likely that there's a typical range of A's, B's and C's.

You're doing fine. Although, if you're truly worried about your grade on a proof, go back and spend some time with it so that you really understand what you did wrong. Once you've received the grade, there's really nothing you can do except work harder/smarter for the next test, so don't fret about your performance.

Think of it this way: if you didn't "have what it takes," you would have bombed the test. You got over 80% of the points, so you must clearly be doing something right.
 
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The only real way to learn how to write a good proof is through experience. Keep practicing and working your way through material. Do what every other math major has to do: buy Rudin and work your way through it. When you come to a Theorem, prove it yourself. If you can't, read a line of the proof and try again.
 
What was the class average?
 
The class average was 80 in my class of 21 students. I just feel like I should be preforming better.

I'll be taking a Rudin-based Honors Analysis course probably my junior year. Next year I'll probably be taking Honors Algebra and another course (intro to topology and differential equations, probably) both semesters, as I've heard algebra is easier to grasp than a lot of analysis.
 
Just do your best and keep pursuing math. Try not to get too bogged down with grades and all that.
 
It really depends on the class. One of my math professors tells a story where he was taking some course (I forget what), and he had trouble with the first test. After getting it back, he saw it was graded 17 out of 100, with a note telling him to see the professor after class.

Needless to say that he was in a right state of panic! He thought he had gotten in way over his head, and had no business being in the class... anyways, he goes to talk to the professor after class, who tells him "Are you sure you're in the right class? You did far better than everyone else, maybe you should take something more challenging?"
 
What were some of your final grades? Lowest grades on midterms, etc.? If you don't mind, of course.
 
Hurkyl said:
It really depends on the class. One of my math professors tells a story where he was taking some course (I forget what), and he had trouble with the first test. After getting it back, he saw it was graded 17 out of 100, with a note telling him to see the professor after class.

Needless to say that he was in a right state of panic! He thought he had gotten in way over his head, and had no business being in the class... anyways, he goes to talk to the professor after class, who tells him "Are you sure you're in the right class? You did far better than everyone else, maybe you should take something more challenging?"
We call that the Keisler Curve at my university. A few semesters back someone in Cal 1 got a 60 on a test by handing in a blank sheet of paper.
 
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A few semesters back someone in Cal 1 got a 60 on a test by handing in a blank sheet of paper.

Wait! Is that true? Sounds like an urban legend or something.
 

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