Is anyone currently doing Further Maths?

[agncsw]

Hi there!

I'm just wondering what Further Maths is like and why you guys decided to join Further Maths (instead of HL). I'm currently in HL Maths and I'm still looking forward to convincing my Maths teacher into *coughs* letting me do Further *coughs more*.

And also what are the differences between Further and HL other than it being harder and deeper on certain topics (especially calculus).

Thanks

[SC2Player]

I'm currently doing Further Maths, and I'll just introduce the structure to you to start with.  

In HL, you have four options (as you probably know).  In Further Maths, you'll do all these four options, as well as two additional topics.  Below is a brief description of each topic Further Maths has.  I've tried to simplify them and explain things where possible, but don't worry if you can't understand some terms or topics - these are not prerequisites.  Googling them may help too.  

1. Sets, relations and groups
   • Overall this is the most abstract topic IMO.  Topics include:
     • Basic set theory
     • Functions (more abstract look)
     • Binary operations (e.g. addition, multiplication)
     • Groups (sets with a binary operation that satisfy certain criteria, e.g. the set of all integers under addition)
2. Calculus
   • Extends the calculus in the HL core.  Topics include:
     • Infinite series
     • Differential equations
     • Taylor and Maclaurin series (a type of series that involves derivatives of a function)
3. Discrete Mathematics
   • This is basically number theory, the study of the integers.  Topics include:
     • Primes
     • The linear Diophantine equation
     • Graph theory
4. Linear Algebra
   • Mostly revolves around matrices, a topic that used to be in the IB core but was taken out in 2014-ish.  Topics include:
     • Matrix properties (definition, matrix addition and multiplication, some common computations for certain matrices, including inverse and determinant)
     • Various methods of solving systems of linear equations
     • Linear transformations
5. Geometry
   • Extends the geometry portion in the core.  Topics include:
     • Advanced triangle geometry
     • Advanced circle geometry
     • Ceva's theorem
6. Statistics and Probability
   • Only topic I haven't done much on, so unfortunately I can't say much on this one. 

Some additional links:

• http://www.ibo.org/globalassets/publications/recognition/5_furthermathhl.pdf (Brief official intro by the IB)
• http://www.sji.edu.sg/qql/slot/u560/Programmes/Academic Programmes/SJI IB Diploma/Six Academic Subject Groups/Further Mathematics HL guide 1st exam 2014.pdf (Official guide, includes all topics to be covered)

Further Maths, in essence, assumes that you've got a firm understanding of pretty much the entire IB HL core.  So, if you think you understand pretty much all of IB HL maths at this point, you're probably set for Further.  The course overall is not very in-depth - it's just a broad look at a number of different common subjects in maths.  Generally a good course to take if you're going to study pure mathematics, or go into a math-intensive field such as a pure science (especially physics) or engineering.  

I myself decided to join because I had already done most of the HL course, as well as some topics in Further Maths, by the start of IB.  So far, it's been fairly straightforward.  

[ABKor752]

I will be going into Further Maths, but I am still in HL at the moment. However, we have been doing Stats and Probability as our option. Here are some things you would learn in that category:

• extended expected-value algebra (not just E(ax+b) but things such as E(aX₁+bX₂)
• sample statistics, and how to use those to estimate population statistics
• linear regressions (which we have not done yet)
• hypothesis testing