Algorithm Finalized, No Explicit Solution Yet

When I started thinking about grad school classes, things were simple. I was going to take combinatorics. After all, it was only offered once every two years! And then I would probably take two core courses or something. Definitely not real analysis, I can study and pass the prelim.


Core courses (Pure Track):

  • Real Analysis
  • Complex Analysis
  • Topology and Manifolds
  • Algebra

For each of these courses, there is a prelim exam.

Requirements: At least two prelim exams: one must be an analysis, one must not be. Take all four courses, except possibly those corresponding to your chosen prelims.


However, at an event just before orientation started, I began to hear some grumbling. Don’t take Topology, they said. The professor is bad. Last time was her first time teaching the course; maybe she’s better now. The applied courses are really good this year; the pure ones will be good next year. The pacing in Algebra was bizarre. Too slow at the beginning, too fast at the end.


Core courses (Applied Track):

  • Mathematical Modeling
  • Numerical Analysis

Neither course has a prelim exam.

Requirements: At least two prelim exams (pure track). Both courses required.


Course conflicts start to be an issue because all math graduate courses are MWF. Combinatorics meets at the same time as numerical analysis, so that is out. Algebra meets at the same time as Modeling. Probability and PDE meet at the same time; neither are core, both seem good?

I meet with my advisor, who helps me to sort through everything. I probably don’t have the prerequisites for Complex, so that leaves only Algebra; I can’t take Modeling either.


Intended Course Registration (Tuesday August 25)

  • Prep for College Teaching (1 credit)
  • Algebra
  • Combinatorics
  • Probability with Measure Theory

Contingent on Topology being inadvisable.


Orientation officially ends; we meet the graduate students. We talk for a long time about courses and professors. I take many notes:

Algebra is graded easy. Don’t take topology, but office hours are good. Complex is average, but next year Brubaker is teaching! Don’t worry about the prerequisites, but wait for Brubaker. Vic Reiner receives a stream of praise: despite enthusiasm about Arnold, Combinatorics finally edges out Numerical.

L-Functions conflicts with Probability. Everyone should take a Paul Garrett course. On the first day, you will figure out if you like the style. Rambles. repeats self often. Provides strong understanding of the shape of the field. Don’t expect to see proofs. Repeats self often. 

Lie Groups receives a very special kind of advertisement: “it is almost always bad”, but this semester it will be good. If you have any interest in anything related to representation theory, take it take it take it take it… Conflicts with Algebra. Shit.


Algorithm for Course Registration (Friday August 28)

  • SIGN UP: Teaching
  • SIGN UP: Combinatorics
  • TRY {
  •      TRY { SIGN UP: L-Functions }
  •      CATCH CannotStandTeachingStyleException { SIGN UP: Probability }
  •      TRY { SIGN UP: Lie Groups } 
  •      CATCH InsufficientBackgroundException { SIGN UP: Algebra }
  • CATCH AdvisorRealizesYoureNotTakingAnyCoreCoursesException {
  •      TRY { SIGN UP: Topology } CATCH CannotStandTeachingStyleException { 
  •           SIGN UP: Algebra
  •           TRY { SIGN UP: L-Functions }
  •           CATCH CannotStandTeachingStyleException { SIGN UP: Probability }
  •      }
  •      TRY { SIGN UP: Lie Groups } 
  •      CATCH CourseConflictException { STOP }
  • }

// Note: the advisor exception can only be thrown if insufficient background is *not* thrown, which means that we do not need to check for it at the end.

// Note: Any outcome of this decision tree results in me signed up for three classes, and one of them is core unless my advisor permits me to take Lie Groups instead of Algebra.

// … Damn this took longer to write than I care to admit.


Seminars continue to be a big uncertainty, but we’ll deal with those later. In any case, I don’t see any conflicts yet between the seminars I want to go to and any courses in the decision tree.

july 22 • 20:03 • maths ➗
I’ve pretty much only been posting maths pictures but it’s really all I’ve been doing! Today I finished re-writing the first sub-unit so I got started on the index at the front. Exam-ridden me in May 2016 is gonna love me for this!

Practice. Go over and over the questions, both the ones from class and the examples in textbooks.

Try to find other questions that are similar to the assigned ones to practice on (e.g. questions from online, or past paper questions).

Make sure that you read all of the text and not just the examples.

Review your errors. When you’re practicing it’s important to identify any mistakes that you make and understand where your skills let you down (e.g. why you made that mistake).

Master the concepts, instead of trying to memorise the processes. It’s important to have a firm understanding of the key concepts underling a topic before moving on to work on another.

Approach problems from different perspectives and try different ways to reach an answer.

Try and keep your notes neat, especially with more complicated maths when you might lose your place, or need to review the material.

Create a study space that is free of distractions. Maths requires a lot of concentration so being able to focus is important.

Create a mathematical dictionary so that you have a list of terms and definitions that you need to know. You can test yourself on this using flashcards.

Because Maths can be so abstract, applying the concepts to a real world situation can really help you understand it.

Form a study group so that you can review material together and test each other. You can even make up problems for each other.

Look for study guides online (sparknotes is a great place to look).

If you have any questions, ask your teacher for clarification. 

Exam tips:

In certain problems, you may be able to “guess” at an approximate answer.  After you perform your calculations, see if your final answer is close to your guess. 

Make sure that you read the questions fully before beginning your calculations. If you don’t pay enough attention you might misunderstand what’s being asked, and lose marks.

Know your calculator! Find out what brand you can use in your exam, buy one, and get used to it! The more familiar that you are with your calculator, the less likely you are to make a mistake.

If you know that your answer to a question is incorrect but you cannot find the mistake, start over on a clean piece of paper.  Often when you try to correct a problem, you continually overlook the mistake.  Starting over will let you focus on the question, not on trying to find the error. 

Remember, that it may be necessary to work out additional information in a problem before reaching the final answer.  These are called “two-step” problems and are testing your ability to recognize what information is needed.

I tend to find most of the study tips and advice out there are mostly related to “written” subjects rather than “calculation-based” subjects, such as maths and as half of my courses are strongly mathematics based I tend to use a different set of study tools to prepare myself for those tests and exams, these are some of my tips for studying maths! (can also go for any calculation-based subjects such as physics): 

1. pay attention in your lectures/classes and take good notes! 

generally in maths classes the lecturer will go over example problems very similar to what you will be tested on, make sure you listen and write down each step as they work through the examples. I tend to add on little helpful notes and tips that that the lecturer mentions in a different colour beside the problem example. 

2. revise your notes to understand the theory

when studying for a maths exam I find what works best is revising the class notes first, understanding the theory (it definitely helps if you understand the application of what you are learning, especially for calc!) and writing down the example problems broken down into each step (if its a long problem). Also learn the formulae you will be given and how to use each one. 

Next, prioritise your study time by spending more time on the topics you understand the least and less time on the topics you understand the most. Revising your notes and the example problems from class should indicate to you what topics you understand and what ones you are struggling with.  


honestly, the best way to learn maths is to just practice as many example problems as you possibly can before your exam! while understanding the theory is helpful, what you’re going to be tested on is your ability to answer a problem. The best way to learn how to do maths problem is by trying the problems yourself. Most courses give out homework problems and example problems to try before the exam, textbooks are also a great source for finding extra problems to do. 

what I like to do is try a few problems using my lecture/theory notes to help me, I will then check my answer and go back through my working to highlight any part that I got wrong and before trying a new problem I will make sure I understand why I got it wrong. Once I’m happy, I then try more problems again using no notes at all! Then I check my answers in the same way. 

I will keep repeating problems this way until I am personally satisfied I can answer what will be in the exam (because everyone is different)

maths all becomes quite simple if you just sit down, understand the theory, and then practice, practice, practice using logical steps.