Intro to Discrete Math - Welcome to the Course!

0:00 welcome everybody in this video I want to give you a little bit of a sense of what the rest of our semester is going to look like I'm going to talk about some discrete math I'm gonna talk about the structure of our course a little bit about how to succeed in the context of this online course so first up what's discrete math anyways I'd like to think of it as a wonderful introduction into mathematical thinking indeed we're gonna learn how to think logically think rigorously to think symbolically and also to think creatively which might seem like this intention with those other things but I don't believe that's the case and indeed in my background I actually start University in computer science and then I took a discrete math course and I kind of fell in love with

0:45 mathematics mathematical thinking and well right now now is the mathematics professor I just take it to the dark side but discrete mathematics takes the sort of set of skills that it applies it to a kind of math problem that's particularly useful for people in computer science of people information technology and the idea of discrete mathematics is in contrast to the kind of sort of continuous mathematics that some of you might have seen in high school or veritable precalculus or a calculus class where for instance if you consider the function x squared that when you think about this in the past we've often thought of it where you're allowed any real number X could be the input not just 1 and 2 but a half and a third and a quarter and pi and root 2 and all sorts of things sort of

1:30 continuous number line of possible inputs discrete mathematics we try to think of the basic entities that we're going to talk about it's sort of separate things like 1 & 2 are separate and they're not connected by the whole set of numbers in between them we might be interested for instance only in the integers numbers like 1 2 3 4 but not necessarily all real numbers the numbers in between it now the reason why discrete mathematics is so important in computer science and information technology is that's how a lot of information technology stuff works for example you have a data base you have just discrete entries and they might have a bunch of different properties but you usually don't have sort of an of 1/3 of the way between two different entries and database and so in this

2:17 course we're going to do all sorts of different things here and do probability we're gonna be doing counting we're gonna try to get to a little bit of graph theory we're just gonna do some basic logic stuff at the beginning of the course of it we feel and powerful and logic and all these different things that have a lot of applications rubbed computer science and information technology now this is an online course and and online courses can be kind of challenging for students because you don't have that constant continuous structure of you got to go to class and you have this sort of social pressure to show up and do whatever the teacher is doing in an online course a lot more that momentum is gonna come from you so I'm gonna give you just a little bit of the scaffolding that I'm going to use in this course that I'm hoping that you can use to master your learning of discrete mathematics so the first part and you've

3:04 probably already seen one of these is the online video and quiz modules and you should think of this as sort of the foundational knowledge this is us establishing the basic idea of whatever section we're going to be doing but it is absolutely not and learning the material to mastery that is telling for you to do you have to take the sort of initial video module as sort of this springboard to become a master in this subject and so the way I sort of structure this is really actually five different components so we've got the sort of the video modules first but then I think is a good idea to go and read the relevant portion of the textbook but not just read of like skimming it read it like really analysing it like what what and why are they saying these things do you have any questions where is this going in the future how do you

3:49 connect this to Prior content and to other content that you know what's the main point of this section why is the little detail valid that's the kind of questions you'd be thinking is you sort of read over this textbooks use it as this introduction for me in the video lectures and then you have to sort of do the deep dive in yourself through the section of the textbook and that's on you and then afterwards I'm going to always create a bunch of practice problems so you have some chance to practice on problems and solutions will be posted but I encourage you to try the problems on your own genuinely as if it was a test but more importantly just because to do mathematics to mathematics you have to do a lot of Mathematica to be sitting there crying problems because it's the problem-solving skill that we're really trying to go for more so than just the answer so we providing solutions and all

4:36 that helpful although I will but what I wanted is for you to focus in on as you try to do the mathematics yourselves and that's the end of every unit I can have an online homework and you're gonna have some system through blackboard where you're going to be able to submit the problems that you've worked on into blackboard and then I'll be able to greet them and that sort of will be the sort of dramatic finish of each individual module so that's the four components the fifth one is going to be the Piazza form a my hope is that we're going to create a quick bit of a community here and the Piazza forum could be for whatever you like if you've got questions on the videos on the practice on the readings and even on the homework oh they'll be a little bit more strict on making sure that we've got academic honesty on that point but but for all these different components you can ask what questions you want and I

5:23 will sometimes see the discussion for questions for you and we have to have a lot of interaction and indeed if you have a lot of interactions I'm gonna get a little bit of credit for this is about 2% of your final grade it's just not a huge amount but just a minimal amount over the course of this semester they were going and helping each other out and working on problems together so I'm excited I think we've got an opportunity for a pretty good course here I hope that you're gonna be excited I think discrete mathematics is really an interesting feel and an important field for people in IT which is what a lot of you presumably are going to be and let's just work on that together and good good luck for sure