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    Hi, which option for Math HL you consider the easiest one?

    I believe Statistics is considered to be one of the easiest, whilst Group Set Theory is one of the hardest. Largely depends if you have a good teacher.

    (Original post by raven)
    I believe Statistics is considered to be one of the easiest, whilst Group Set Theory is one of the hardest. Largely depends if you have a good teacher.
    Well, I've done Further Maths so I know all the current options. But abstract algebra (sets, relations and groups) is one of the easiest ones I should say.
    In order of difficulty I would rank them so (easiest first):
    1. discrete maths
    2. sets, relations and groups
    3. statistics
    4. analysis and approximation
    5. Euclidean geometry and conic sections

    Statistics is somewhat tricky really. It's not at all difficult conceptually; the only real problem I have had with it was knowing whether my result was right. Everywhere else it is relatively easy to make sure you get the needed result by either using common sense or the GDC; in statistics you get some number and you have no way of being sure it is appropriate.

    Now, if you have the HL Maths exam after November, you will have somewhat different options available. The most horrible, devilish one, Euclidean geometry, has been scrapped (unfortunately so have conic sections, which were rather nice). I think iterative methods (fixed point iteration, the Newton-Rhapson method) in analysis have been scrapped in favour of further differential equations (in addition to those done in HL Maths, you do first order by means of an integrating factor and second order differential equations, I believe).

    Of course in the end it is very difficult to say which option is difficult and which is easy, because every time you get different tasks and some may be more difficult in a given examination session than others. This year in the HL Maths exam all options were trivial (they compensated for the other tasks which were much more difficult than usually, I suspect). In the Further Maths exam though, I'd say geometry was quite easy; analysis was very easy; statistics was easy; but both discrete maths and some of the abstract algebra were unusually difficult.

    Let me outline some of the things you're going to do in each of these topics.

    1. Discrete maths is usually quite easy; it is about the number theory and the graph theory. You do things such as the division theorem, the Euclidean algorithm (for finding gdc and lcm as well as for changing number systems (binary, octal, hexadecimal)), linear diophantine equations, recurrence relations and similar in number theory; and graphs, trees, and problems with these (eg, the travelling salesman problem) in graph theory. The graph theory is very different from 'standard' school maths in the approach used and is really quite lovely. If you can choose, discrete maths is definitely the way to go!

    2. Sets, relations and groups is what we did in HL Maths (as opposed to Further Maths where we covered the other four options) and it is supposedly the most popular option. It's about abstract algebra: axioms of groups, relations and their properties, equivalence classes, etc. Some of the proofs can be a bit tricky sometimes, but more often than not they'll be adaptations of the proof you'll have done for Lagrange's theorem. This option seems quite boring at first because you don't see any possible practical applications and a lot of the problems have the same basic approach to them, but I like it nevertheless. It's rather abstract, however, so if you've had problems with, say, complex numbers, you probably don't want to take this.

    3. Statistics is, well, not done very much where I'm from, not even at university level, because it is seen as not very mathematical. So it wouldn't normally be very popular. But it's not at all demanding mathematically: normally you just state things without proof (which is almost blasphemous for our teachers of maths). It's probably the least difficult to understand, though as said, you can never know if your result is correct. But the result usually only brings one mark in the exam, so that isn't so terrible if your method is approximately correct. Nothing particularly advanced is done: the Poisson distribution, significance testing, chi-square fit and independence testing, etc.

    4. Analysis and approximation is all very lovely when you learn it. It's not really difficult contentwise, but I think this is the topic which has had, overall, the most devilish exam tasks. You'll learn about convergence tests of infinite series, alternating series, Taylor and Maclaurin series and polynomials, power series; numerical methods of integration (Newton-Leibniz, trapezium and Simpson's rules); and iterative methods for finding zeroes of composite functions (Newton-Rhapson method, fixed point iteration).

    5. Geometry is hard! You get some sort of circle with a lot of triangles and then you have to prove something from it. Usually the answer goes something like 'We draw this magical line ... and then we see this and that.' The main problem in geometry is seeing where to draw this magical line. It isn't THAT difficult to learn that you should always attempt to see if you can manage to squeeze in the harmonic ratio, Ceva's or Menelaus' theorem - these seem to be their favourites. But although proofs aren't that difficult in themselves (if you can draw nice pictures of course), the main problem I have with geometry is that there is always this risk involved that you won't 'see' what you have to do. Sometimes you just stare at a situation and can't think of anything else to try: you just don't see 'it'. And that's a risk I wouldn't want to take for the HL Maths exam. Especially because in the past few years no one has taken geometry except for a few of those who didn't do any option in class at all (well, according to subject reports at least), so they don't really care that the tasks are almost impossible to solve. The Further Maths tasks, which aren't by choice, are much easier in comparison.
    As for the conic sections (ellipse, circle, parabola, hyperbola), they aren't usually that difficult, but they do require a lot of algebraic competence. The equations you have to simplify tend to be quite complicated.

    How come you get to choose the option though? Doesn't your teacher select it for you? (We didn't get to choose any of the options in any subject.)

    In our school our teacher selected Analysis and approximation. Some of us did not like it and decided to study another option. So few of us did geometry and one of us did discrete mathematics.
    If you are not graduating in N05, then you have these options: Statistics and probability; Sets, relations and groups; Series and differential equations; Discrete mathematics. From these I would probably recommend Discrete mathematics. My friend who did it says it is quite easy.

    I assume that you are talking about the new 2006 syllabus. If so, I would consider the Series and Differential Equations Option to be the easiest. If you have a sound background in Calc., go for it. I took AP Calc. AB at my school and it covered quite a large portion of the content. Personally, I dont think its all too hard to learn. You have Taylor series, Maclaurin series, differential equations (obviously) and even slope fields! It may also be helpful if you look at the syllabus and decide for yourself what the easiest option may be.

    Are you so luck to select the option by yourself? I had no choice because my teacher chose the same option for all of us who study IB in our school...
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