Starting Postgraduate Programme in Economics, Advice for Calculus - Real Analysis

In summary, the individual is starting a postgraduate level Economics course and will have to go through a 10-day Math Camp beforehand. The curriculum includes topics such as real analysis, metric spaces and topology, linear algebra, and optimization. The individual wants to prepare as best as they can for the curriculum and is seeking advice on where to start with their studies. They are recommended to review basic analysis and linear algebra, with suggested resources such as free online lecture notes and the book "understanding analysis" by Abbott. It is advised to ask a lot of questions and put in as much time as possible to be well-prepared for the course.
  • #1
nosfnosf
2
0
Hello,

I am starting a postgraduate level Economics course in two months. I will have to go through some kind of a Math Camp before the course, lasting more or less 10 days. Here is my curriculum;

1. REAL ANALYSIS

Topics:
• Sequences and Convergence
• Function on Rn
• Continuity
• Differentiability
• Riemann’s Integral

2. METRIC SPACES & TOPOLOGY

Topics:
• Metrics and Metric Spaces
• Open and Closed Sets
• Compactness
• Connectedness
• Fix Point Theorems


3. LINEAR ALGEBRA

Topics:
• Vector Spaces
• Linear Applications and Matrix Representation
• Matrix Calculus
• Projections
• Eigenvalues and Quadratic Forms

4. OPTIMIZATION

Topics:
• Convex Sets
• Convex and Concave Functions
• Unconstrained Maximization
• Contrained Maximization, Lagrange’s Method and Kuhn-Tucker Theorem
• Dynamic Programming

----------------------------------------------------------------------

Now, I want to prepare as best as I can for this curriculum since success at these coursese will affect bursary levels. I took a few courses at undergraduate level for calculus but just consider I am almost new to these topics and I want to start over from beginning with a good Mathematical mind, want to get these concepts before I begin the curriculum.

What are your suggestions at this point? Should I start from calculus or real analysis? Any advice for some links or lecture notes online?
 
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  • #2
Hi nosfnosf! :smile:

Reviewing calculus is useless in my opinion. Just make sure that you're comfortable with the notions of integrals, continuity, derivatives. You just need to know what the concept means and you just need to calculate the basic examples. That'll be enough.

If I were you, I would start reviewing some basic analysis and linear algebra. Here is a site with many free lecture notes:
For analysis: http://hbpms.blogspot.com/2008/05/stage-3-introductory-analysis.html
For linear algebra: http://hbpms.blogspot.com/2008/05/stage-2-linear-algebra.html
Just check a few free lecture notes and see which one you like.

If you prefer a book: the book "understanding analysis" by Abbott is written for people like you!

Anyway, analysis and linear algebra aren't the easiest topics if you've never seen much math before. That's why I want to encourage you to ask a lot of questions on the material.
 
  • #3
micromass said:
Abbott is written for people like you

=OO

!

(lol)
 
  • #4
micromass said:
Hi nosfnosf! :smile:

Reviewing calculus is useless in my opinion. Just make sure that you're comfortable with the notions of integrals, continuity, derivatives. You just need to know what the concept means and you just need to calculate the basic examples. That'll be enough.

If I were you, I would start reviewing some basic analysis and linear algebra. Here is a site with many free lecture notes:
For analysis: http://hbpms.blogspot.com/2008/05/stage-3-introductory-analysis.html
For linear algebra: http://hbpms.blogspot.com/2008/05/stage-2-linear-algebra.html
Just check a few free lecture notes and see which one you like.

If you prefer a book: the book "understanding analysis" by Abbott is written for people like you!

Anyway, analysis and linear algebra aren't the easiest topics if you've never seen much math before. That's why I want to encourage you to ask a lot of questions on the material.

Thanks for the reply.

So you think it will be enough for me to learn basics of these concepts? I was thinking learning these topics almost full. Will these links provide them to me considering I have two months to prepare and can study a few hours a day? I will try to get the book from libraries too.
 
  • #5
nosfnosf said:
Thanks for the reply.

So you think it will be enough for me to learn basics of these concepts? I was thinking learning these topics almost full. Will these links provide them to me considering I have two months to prepare and can study a few hours a day? I will try to get the book from libraries too.

The more you know about the topic, the better prepared you will be. So learning the topics almost full would be the best choice. But knowing the basics should get you there too. It's a matter of how much time you're willing to put in :smile:
 

1. What is the difference between a postgraduate programme in economics and an undergraduate programme?

A postgraduate programme in economics is typically more advanced and specialized than an undergraduate programme. It may involve more independent research and in-depth analysis of economic theories and models. Additionally, postgraduate programmes often require a higher level of mathematical proficiency, making courses like calculus and real analysis crucial for success.

2. How important is calculus and real analysis for a postgraduate programme in economics?

Calculus and real analysis are essential tools for understanding and analyzing economic theories and models. These mathematical techniques allow economists to solve complex equations and make predictions about economic phenomena. Without a strong foundation in calculus and real analysis, it can be challenging to excel in a postgraduate programme in economics.

3. What advice do you have for students who struggle with calculus and real analysis?

If you are struggling with calculus and real analysis, it is essential to seek help as soon as possible. Talk to your professors or teaching assistants, join a study group, or hire a tutor. Practice regularly and do not be afraid to ask questions. These concepts may be challenging at first, but with dedication and persistence, you can improve your understanding and excel in your postgraduate programme.

4. Are there any online resources or tools that can help with learning calculus and real analysis?

Yes, there are many online resources and tools available to help with learning calculus and real analysis. Khan Academy, Coursera, and MIT OpenCourseWare offer free online courses and tutorials on these subjects. You can also find practice problems and solutions, video lectures, and interactive simulations to help you understand these concepts better.

5. How can I apply calculus and real analysis to real-world economic problems?

Calculus and real analysis are used extensively in economic research to analyze data, build economic models, and make predictions about economic phenomena. As a postgraduate economics student, you will learn how to apply these mathematical techniques to real-world problems and develop a deeper understanding of economic theory and policy. Additionally, many careers in economics, such as economic research and analysis, require a strong foundation in calculus and real analysis.

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