Getting Ready for Mathematical Classes in the New Semester – Guest-Blogging on SFU’s Career Services Informer

The following blog post was slightly condensed for editorial brevity and then published on the Career Services Informer, the official blog of the Career Services Centre at my undergraduate alma mater, Simon Fraser University

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As a new Fall semester begins, many students start courses such as math, physics, computing science, engineering and statistics.  These can be tough classes with a rapid progression in workload and difficulty, but steady preparation can mount a strong defense to the inevitable pressure and stress.  Here are some tips to help you to get ready for those classes.

(For the sake of brevity, I will denote all classes that require mathematical thinking and problem-solving as “mathematical classes” in this post.)

Review Pre-requisite Material

  • Mathematical classes are very cumulative.  Before your classes begin, or during the first week, take some time to review the pre-requisite materials.  Read each course syllabus to get a sense of the most important pre-requisite topics.  Then, review your notes and textbooks, re-write the foundational definitions, theorems and proofs, and solve some typical problems from past courses.  If you remember your pre-requisite topics well, try to do some introductory examples of the most important topics in your new courses’ textbooks.
  • It’s better to review a broad range of past topics rather than dive deeply into one specific area, since this review’s goal is to simply brush up on relevant skills.

Get to Know the Language Again

  • Mathematical classes have their own written language.  It’s really a more compact form of writing the same thing in English.  For example, an earlier video tutorial on my blog introduced the definition of the hazard function1 for continuous survival data:

h(t) = \lim_{\Delta t \rightarrow 0} [P(t < X \leq t + \Delta t \ | \ X > t) \ \div \ \Delta t].

Here is what it means in words:

The hazard function – a function of time – is defined as the limit of a fraction as some change in time, \Delta t, approaches 0; this fraction has the following numerator and denominator:

– the numerator is the probability that the random variable X lies in some interval greater than t but less than or equal to a later time t + \Delta t, conditioned on the event that X is greater than t

– the denominator is the change in time, \Delta t.

Phew!  What a big mouthful2!  This is why mathematical notation exists – a simple line can capture an enormous smorgasbord of words and concepts in a much more succinct and visually clear way.

  • Familiarize yourself with writing in the language and notation of your particular subjects again.  It’s like learning any other language – if you haven’t used it for a while, you can always pick it up again with a little review.

Practice Computer Programming

  • If your course has a computer programming component, learn or practice that language.  Get used to the basic syntax and write some basic scripts and functions.
  • For a more in-depth review that will also help you with your new course, search online for assignments and solutions in the same versions of your course from previous semesters.  Find a programming exercise to practice, and do each exercise line by line.

Keep Old Textbooks (or Borrow From the Library)

  • Many higher-level mathematical classes are just harder and more in-depth versions of lower-level classes, so your earlier textbooks might explain concepts more clearly.  My graduate statistics classes had some very badly written textbooks, so I abandoned them entirely and relied on my undergraduate textbooks instead – they explained the concepts to almost the same level of depth, but with much more clarity.

Perfect Your Study Space

  • Studying for mathematical classes requires intense concentration and prolonged sitting.  Get a comfortable, spacious and ergonomic desk in a properly lit room that suits your desired noise level.  Find a “go-to” study spot on campus where foot traffic is low.  My favourite place to study on the Burnaby campus was the first floor of the Bennett Library.  It is very quiet and often has seats available.

Schedule in Breaks

  • Get a timer to remind yourself to take breaks and drink water every 15-20 minutes.  Lethargy and dehydration are two of the worst enemies of productivity, so make sure that you get up regularly and walk around for a few minutes while drinking plenty of water.  Avoid coffee or soft drinks – they can cause dehydration.

Use a Book Stand

  • One of the best investments that I ever made in university was a book stand.  Before buying one, I had to hunch over to read my textbooks – this caused neck strain and reduced blood flow to my head, hastening fatigue.  By reading a book in an (almost) vertical position, I can keep my head in its natural upright position.  This subtle adjustment made studying a lot more pleasurable and improved my productivity significantly.

Scrap Paper is Your Best Friend

  • Reading and studying from a textbook requires a lot of writing of definitions, theorems, proofs, expressions, equations and calculations.  Prepare a thick stack of scrap paper on your desk and a paper recycling box within an arm’s reach.  To reduce wasting paper, I often gathered stacks of scrap paper from the large recycling boxes near printers and photocopiers in the library or computer labs.

Get Help

Take Care of Yourself

  • Set a regular routine for sleeping, eating, relaxing and exercising.  Your brain will absorb concepts a lot better when you are well nourished and alert.  Studying for one hour with a healthy brain and an energetic body is far more productive than studying for two hours with a sleep-deprived brain and a lethargic body.
  • Self-care is one of the most neglected aspects in students’ lives, and it’s a lot harder to correct bad habits in the middle of a semester.  Take advantage of the time at the start of the semester to establish a good routine before the onslaught of assignments and midterms becomes overwhelming.  The SFU Health and Counselling Services Blog offers many tips and resources.

When You’re Feeling Down

  • Your life may already be stressful with personal and professional obstacles, and challenging math-oriented classes can exacerbate that stress.  If you’re feeling overwhelmed by the pressure, consider attending SFU Health and Counselling Services workshops or speak with one of their trained Counsellors.  Even with my success at SFU, there were times when I felt overwhelmed by the stresses of my coursework, and I found the counselling services to be very helpful.

Footnotes

  1. If you will take intermediate mathematical statistics (STAT 330 at SFU) or any course at a higher level, then you will be expected to understand the above notation.  You would have learned to understand the above notation from introductory statistics and calculus classes, so review concepts like limits, probability, conditional probability and random variables if needed – you will also encounter the necessary language and notation to understand the above equation.
  2. Students of statistics and probability may realize that the above equation can simply be written ash(t) = f(t) \div S(t), where f(t) is the probability density function and S(t) is the survival function.  My follow-up video tutorial explains why the hazard function can be written this way, and I have another video that shows some useful mathematical relationships between any pair of h(t), f(t), and S(t).

Your thoughtful comments are much appreciated!

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