Which advanced math courses are favored by top graduate programs?

In summary, The individual is a math and chemistry major at the University of Illinois Chicago and is looking to plan their advanced math courses for graduate school admission. They are considering courses in applied mathematics, engineering, and physical chemistry, and are seeking suggestions for courses that would give them an edge in these fields. They are also wondering if a course in Advanced Calculus would be beneficial and if courses in Statistical Methods or Statistical Theory would be more rigorous. They also ask about the type of mathematical training a school like MIT would want for graduate studies in physical chemistry, engineering, or geo studies. Advice given includes taking Numerical Analysis, PDEs, and Advanced Calculus for the applied route, and Analysis II and Abstract Algebra II for pure math.
  • #1
ryanj123
24
0
Hey all.

I'm actually a math and chemistry major at the Univ. of Illinois Chicago. I have a competitive GPA, research experience, and an overal good academic history. What I'm trying to do is plan my advanced math courses to not only be functionable within my area of interests (engineering, applied mathematics, physical chemistry), but are respected and appreciated by graduate admission review boards.

Here are my options.

Analysis II
Topology I & II
Linear Algebra II
Abstract Algebra II
Partial Differential Equations
Complex Analysis
Probability Theory
Statistical Theory
Mathematical Models
Numerical Analysis
Advanced Calculus
Differential Geometry

Any suggestions not listed?

So within the fields of applied mathematics, engineering, and chemistry which would give me the best edge?
 
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  • #2
If you are going for the applied route rather than looking into pure mathematics, Numerical Analysis, PDEs, and Advanced Calculus (assuming you mean vector calculus) are good choices (Numerical Analysis and Advanced Calculus are usually required courses for applied math modules). Complex Analysis and Functional Analysis are also good courses to have.

As for the pure math courses you mentioned - Topology, Analysis, Complex Analysis, Abstract Algebra, and Differential Geometry - they are definitely useful for pure math degrees - in fact all of them (except possibly Differential Geometry) should be taken if you are looking into grad school for pure math. Ring Theory, Field Theory, and Measure Theory are also good courses in pure math. But if you are deciding to go for applied math, most of these courses won't be as useful as taking upper year applied math courses.
 
  • #3
Since my question is related to the OP's line of inquiry, I hope I'm not hijacking this thread. Is Advanced Calculus usually a course on multivariable calculus/vector calculus? I have taken a rigorous calculus course this past year and I plan to take a rigorous real analysis course this upcoming year. Our school doesn't really offer an honors multivariable calculus course, nor does it have an advanced calculus course. Although I have been reviewing more introductory analysis topics and studying topology on the side, should I work through an advanced calculus text? I have a good grasp of the computational aspects of multivariable calculus, but I will be going through calculus on manifolds by spivak in my real analysis course next year, I think. Thanks.
 
  • #4
For admission to graduate school in mathematics. Of the ones listed, the essentials would be Analysis II, Abstract Algebra II. plus subject matter GRE.
 
  • #5
VeeEight said:
If you are going for the applied route rather than looking into pure mathematics, Numerical Analysis, PDEs, and Advanced Calculus (assuming you mean vector calculus) are good choices (Numerical Analysis and Advanced Calculus are usually required courses for applied math modules). Complex Analysis and Functional Analysis are also good courses to have.

As for the pure math courses you mentioned - Topology, Analysis, Complex Analysis, Abstract Algebra, and Differential Geometry - they are definitely useful for pure math degrees - in fact all of them (except possibly Differential Geometry) should be taken if you are looking into grad school for pure math. Ring Theory, Field Theory, and Measure Theory are also good courses in pure math. But if you are deciding to go for applied math, most of these courses won't be as useful as taking upper year applied math courses.

Thank you for the advice. I agree with you on the applied path, as pure mathematics is something I really don't see in my future (although appreciated of course). Are you familiar with any applied courses that are respected in the physical sciences besides the basic Calculus sequence and Differential Equations? I hear a second course in Linear Algebra, sometimes Complex Analaysis... each opinion varies.

And does anyone know if a course in Statistical Methods or Statistical Theory would be more rigorous?

Does anyone know the type of mathematical training a school such as MIT would want for let's say graduate chemistry (physical), engineering, or geo studies?
 

1. What are the most commonly required advanced math courses for graduate programs in science, technology, engineering, and mathematics (STEM) fields?

The most commonly required advanced math courses for graduate programs in STEM fields include calculus, linear algebra, differential equations, and mathematical analysis. These courses provide a strong foundation in mathematical concepts and techniques that are essential for further study in the STEM disciplines.

2. Are there any specific advanced math courses that are highly valued by top graduate programs?

While the specific requirements may vary between graduate programs and institutions, courses like real analysis, abstract algebra, and topology are often highly valued by top graduate programs in STEM fields. These courses delve into more complex and abstract mathematical topics, preparing students for advanced research and problem-solving in their chosen field.

3. How important is it to have a strong background in advanced math courses for admission to top graduate programs?

A strong background in advanced math courses is typically considered a key factor in the admission process for top graduate programs in STEM fields. These programs often have a rigorous curriculum that requires a solid understanding of advanced mathematical concepts. Additionally, a strong math background may demonstrate a student's analytical and problem-solving abilities, which are highly valued in these fields.

4. Are there any other factors besides advanced math courses that can improve a student's chances of being accepted into top graduate programs?

While a strong background in advanced math is important, it is not the only factor that top graduate programs consider in their admissions process. Other factors that may improve a student's chances include research experience, letters of recommendation, and a strong academic record in relevant coursework. Additionally, having a well-rounded profile with extracurricular activities and relevant work experience can also make a student stand out to admissions committees.

5. Are there any resources or study strategies that can help students prepare for advanced math courses in graduate school?

There are many resources and study strategies that can help students prepare for advanced math courses in graduate school. Some strategies include seeking out additional practice problems, attending study groups or tutoring sessions, and utilizing online resources such as video lectures or interactive tutorials. Additionally, staying engaged and seeking help from professors and classmates when needed can also significantly aid in understanding and mastering advanced math concepts.

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