 Hi everyone, it's MJ and welcome to this course on foundational mathematics for actuaries. And I thought what better way to start this video than to give an analogy which my very own lecture gave to me with regards to mathematics and actuarial science. And he said that mathematics for an actuary is like fitness for a soccer player. It's not the only thing you need but you can't play a full match without it. So many people sometimes think that actuarial science is only about maths and that's not true. You definitely need maths if you want to be an actuary but there's a whole bunch of other things that you need to learn as well. Now what I'm going to be doing is building this course based on the syllabus set by the International Lectorial Association with regards to foundational mathematical topics. So I kind of took their syllabus online and created the course based on that. So let's look at the syllabus in a higher level and then we're going to go into a little bit more detail for each of these topics. So we have functions and sets. We've got differentiation, integration, sequence and series, differential equations which are probably the hardest one. Then we have real and complex numbers, matrices and systems of linear equations, vectors and vector spaces and inner product spaces and finally probability. Now let's like I say have a little bit of a deep dive in each of these topics. So when it comes to functions and sets and this kind of makes up 10% of the syllabus, here we need to define a function, apply functional concepts such as domain, co-domain, image, limit, inverse. We need to know what asymptotes and turning points are and how to find them. We also need to know set terminology as well as concepts and we need to calculate the roots of equations and evaluate integrals. Then if we come to differentiation which kind of makes up 10% of the course as well, here we need to find the derivative of a function as a limit. We need to look at the derivative of a function from first principles. We need to be familiar with the chain rule, partial derivatives, derivatives for various functions such as power, trigonomic, exponential, logarithmic, hyperbolic, guys these names are quite a little bit difficult to try and roll them all of the tongue but you also want to look at extreme points of a function of two variables and this one's probably also a little bit complicated and difficult to pronounce but we're going to try and use Lorraine multipliers for constraint problems and that's probably that's where you want to get to with differentiation is that one and we will of course do a couple of examples in the course. With regards to integration we need to evaluate integrals and this can be both definite and indefinite integrals. We're going to be looking at the substitution technique as well as integration by parts technique and then we'll also look at how to evaluate double and other multiple integrals. We'll also look at how to calculate the areas and volumes of geometric shapes and evaluate multiple integrals and interchange the order of integration and apply various techniques such as the trapezium rule and the Simpsons rule. Then when it comes to sequences and series also again about 10% you can see the syllabus is quite evenly spread. We've got the Taylor and Maclaurin expansions for functions of one and two variables very very important when you do mathematical statistics especially around moment generating functions. They are quite tricky though. I'm not gonna like Taylor and Maclaurin expansions. I even struggle with them a little bit but we also need to define sequences and series. We need to look at concepts such as boundedness, convergence, limits, monotocity as well as looking at formulae for the sums of arithmetic and geometric progressions and techniques to determine the convergence or boundedness. Then we move on to differential equations where we need to solve first order differential equations. This can either be separable, linear or homogeneous and as well we want to solve first order differential equation models for various applications such as when we've given conditions or when we need to find the values of parameters. Then real and complex numbers only makes up 2% and we just need to carry out arithmetic with complex numbers isn't too difficult and then moving I guess to a big chunk which is 20% is matrices and systems of linear equations. Here we're going to be doing matrix operations such as addition, scalar multiplication, matrix multiplication and transposition. We also need to calculate the determinants of a matrix. We're going to need to know how to use Kramer's rule to solve a system of linear equations as well as Gaussian elimination to find the rank of a matrix, inverter matrix, solve systems of linear equations as well as looking at eigenvalues and eigenvectors and we use them to compute the characteristic polynomial of the matrix. We also need to determine whether a matrix is diagonalizable and we need to find a diagonalizing matrix. Then when it comes to vectors, vector spaces and inner product spaces this is 5%. Here we need to do vector operations which is addition, scalar multiplication, vector product, scalar triple product, vector spaces, inner product space and orthogonality. Like I said the pronunciation of some of these things is a bit tricky but your probability 25% and this of course has expanded greatly in mathematical statistics. So some basic concepts, set functions, sample space and event, the basic axioms of probability, we know how to calculate probabilities, how to use the addition rule and union of two events, conditional probability, Bayes theorem and correlation versus independence. And the thing is your mathematical journey with regards to actuarial science is not over yet. So even after you've gone through this course and you've gone through all of these topics it's not the end because once you've done these you're then ready for the actuarial subjects and these are like mathematical statistics, financial mathematics, stochastic calculus and there's many other topics as well but you need to know these foundational topics before you can attempt those. And let's maybe end with a nice little quote which says in maths the art of asking questions is more valuable than solving problems and that's from Gagore Cantor and we're going to be starting set theory which is Gagore Cantor's little baby and we're going to be talking all about it and how it is the foundation of mathematics. So if you're still watching this video it means you're coming from YouTube and you would have realized that this is the very first video for my foundational maths for Actuaries course which is on Udemy. So make sure you go to Udemy and check it out. It still is in the early days so I'm still constructing it. I think that's why my rating is only 4.1 because we got a whole bunch of students just through Udemy's natural search engine and they're probably like penalizing me for not having everything completed yet but at the moment we have got set theory and functions which is some nice pre-calculus. Then we do have a bunch of videos on differentiation as well as integration as well as differential equations. So we basically have all of the calculus. I still need to film and record the linear algebra. The videos or the presentations have been done. I actually find time to do the recording and then I will upload it onto Udemy as soon as that is done. What I'm also doing is turning it into a maths study aid. I don't want to say textbook because I've taken a very informal approach to trying to explain everything rather than having theorems and diagrams and trying to be too accurate that it becomes a little bit confusing like you sometimes get in a traditional textbook and this book is also as you can see there it's an early pre-release edition. It's not completed yet and you can see still very much early days but this is me releasing the video now. I know these videos you know stay on YouTube for a long time so if you're watching this like a month after it's released then everything's probably already out there which means you can head to Udemy. I'll put the links in the description below to watch the video series. You can go to Amazon Kindle again I'll put a link there if you want to rather just read and it's at the moment it's 50 pages. Once it's finished I can't see it being more than 60-65 so it's straight to the point. It's a very very thin maths textbook thing that we're covering so many things but like I say I want to get straight to the point and very mindful of your time and then final thing to just say is that if you're part of the Actuarial Society then contact them because you'll be able to get all of these videos for free. So part of the Actuarial Society, the Academy is all the students will get to watch these videos for free through them but if you are coming from outside the Actuarial Society you can still access them either through Udemy or like I say if you want to read it through Amazon Kindle. As always thanks so much for watching and I'll see you guys soon. Cheers!