 So let's spend a few minutes talking about the topics that we'll cover in the physical chemistry course. So physical chemistry typically includes a large variety of different topics, many examples of which are on the screen right now. So this is sort of a grab bag of topics, different textbooks, different courses cover these topics in different orders and that can often seem a little bit arbitrary. So that can be made a little less arbitrary if I color code these topics based on categories. So some of these topics fall in the area of thermodynamics, things you've likely heard of before like entropy and free energy. Other topics fall in the topic of quantum mechanics, things like the harmonic oscillator, the rigid rotor, the hydrogen atom or quantum mechanical topics. And then there's another category of topics that are applications or sort of miscellaneous topics. So this list, color coding this list suggests that you can order the topics in a somewhat reasonable way and this is the way that many textbooks, many courses order the topics in sort of a traditional format. So the thermodynamic topics might appear in the first semester of a two semester course, the quantum mechanical topics appear in the second semester of the course, again traditionally. And then this collection of miscellaneous and application topics sort of are a grab bag, they might be included in a rushed form at the end of the second semester or they might be included if the instructor has a particular interest in those topics or they might sometimes just be left out altogether. There's a disadvantage with this approach which is that in fact the thermodynamic topics, many of these thermodynamic topics can be explained or introduced if you know the quantum mechanics first. So in fact the quantum mechanics explains why the thermodynamics behaves in the way it does. So that suggests that there's a different order that you could use to order a physical chemistry course and this is a more modern approach that's called quantum first. So more modern textbooks have been leaning towards this quantum first approach where the first semester, the first half of the book describes all these quantum mechanical topics. The second semester explains the thermodynamic topics and again these extra application topics get thrown in whenever there's time. There's a pretty distinct disadvantage with this approach too which is that you spend the whole first semester, three months or so, talking about nothing other than quantum mechanics. Quantum mechanics is full of a lot of math, it's fairly abstract, some people like it but a lot of people very greatly dislike it. So having to do three months worth of quantum mechanics before you begin to see the results, the applications of how you apply quantum mechanics to explain applications or to explain topics like free energy can be a little daunting and a little bit intimidating. So that's clearly got some disadvantages as well. The good news is there's an easy way around both of these disadvantages of these two different orders and that's to notice that the link in fact between the quantum mechanics, the thing that lets us explain why quantum mechanics explains much of thermodynamics relies on these two topics, the Boltzmann distribution and partition functions. So if we treat those topics explicitly rather than just some extra topic thrown in at the end if we have time, then it lets us order these topics in a much more intuitive way, treat those topics up front. So instead of a quantum first approach, this is more like a Boltzmann first approach to quantum mechanics. And so after a brief introduction or review of some thermodynamic topics and introduction of these statistical mechanics or Boltzmann topics, then we're ready to just get a little introduction to some quantum mechanics at which point we can explain why quantum mechanics explains ideal gases and things about simple gases and some other features of thermodynamics. Then a little bit more quantum mechanics helps us explain a lot more thermodynamics and then more advanced quantum mechanical topics help us explain several additional applications or thermodynamic topics. So the key here is we're interleaving, we're mixing, hopping back and forth between some thermodynamics and some quantum mechanics and back and forth. So you don't have to spend a whole semester diving into the details of quantum mechanics before you use it for interesting things. It means discussions of applications are never very far behind the theoretical topics that you need to understand them. And I think it leads to a much more intuitive and easy to understand and enjoyable way of approaching physical chemistry. One thing that does mean, however, if we're going to do this Boltzmann first approach is some of the first topics we need to include are some, so a little bit of math that we need to introduce this idea of the Boltzmann distribution. So the very first step is going to be to start with a little review of topics that you may have seen before or might be new to you in the area of probability. So the next thing we'll do is we'll start with some review of probability topics.