# Introduction to a university course, including initial setup and an overview of the curriculum and tools ## Course Introduction and Overview ### Pre-session technical checks and preparations - Instructor (8/26/25 5:17 PM): I'll be right back. Please scan the QR code. ### Opening remarks and instructions for audience participation - Instructor (8/26/25 5:17 PM): Okay, we're about to begin. - Instructor (8/26/25 5:17 PM): I hope everybody uh was able to scan the QR code or log into Slido. If you haven't, please do so now. - Instructor (8/26/25 5:18 PM): Thank you. ### Instructor introduces himself and outlines the course agenda - Instructor (8/26/25 5:18 PM): So, um, welcome to CIT 5920. Um, it's nice to see you all. Um, so this is officially called Mathematical Foundations of Computer Science, but that sounds a little bit um uncool. So I like to call this course how to communicate formally with discrete math. - Instructor (8/26/25 5:18 PM): So I'm Jérémie Lumbroso. Um, and so I'll be your instructor this semester in this course. - Instructor (8/26/25 5:18 PM): So the agenda today is I'm going to introduce myself. I'm going to try to explain the why behind this course, what we're going to be doing. Uh, I'm going to give you an overview of how the course will work and what the expectations are. Um, and um, we'll practice the participation tool. Uh, and I'll talk a bit about key policies and resources. Um, I will also, so I know some of you are also coming here because you want to figure out what the waiver exam is and I'll also mention that um in the slides. - Instructor (8/26/25 5:19 PM): So, um, as we just, as I just mentioned, um, I use Slido. Um, it's a big part of how I teach and I use it in a couple of ways. The main way is to take your questions. Now, I could just go on and go on and read a discrete math book and it would always be the same. What is different is you, the students. It's how you understand and don't understand what I'm saying and it's when you ask me questions that I understand what I'm doing wrong and then I have an opportunity to correct. So, I know it's intimidating to ask questions and that's why I use this tool so that you can enter questions from the comfort of your phone. So, please do take me up on it. Um, my courses in this particular NCIT 5920, sometimes I spend 30 to 40 minutes answering questions and that's fine because you can always go and read a book, you can always go and ask chat GPT, but here you will have my explanations that are really customized on 15 years of teaching and what exactly you need to know in the MCIT program. So, please do take advantage of that. If you're not ready to ask questions, you can also upvote other people's questions and that signals to me that answering that question would benefit more than just one person. And whenever you post, you can choose to be anonymous, but there's really no reason to be to do so because asking a question is always a very constructive, uh, it's a very constructing thing to do and the main thing that you're learning about in this course is to communicate formally. So asking questions in this course is a good start. Finally, um, I will every now and then ask you polls and also give you short quizzes and the only thing I want you to know is that none of them are graded. Um, so whenever there's a quiz, the point of the quiz is to get you to understand whether you've heard me right and that's all it's meant to do. ### Instructor's personal background and career journey - Instructor (8/26/25 5:21 PM): So, I'm Jérémie Lumbroso. I'm originally from France. Um, um, I'm a dual citizen. My mother was American, so I I was always um a little bit in both countries. Uh, but I ended up taking a job um because in France there were no jobs and there were no jobs for me. I took a postdoc in Vancouver first at Simon Fraser University and then I I was a faculty at Princeton for about nine years and I joined Penn two or three years ago. So this is my third some a third year and um I'm really I I love teaching this course and um I I still feel like I just joined. Um, I've also been interested in education uh from a startup point of view. I've had two startups. Um, one of them is called Code Post and it's uh to grade code, to do code review and the other one is called uh Qvids. ### Instructor's teaching philosophy and neurodivergence disclosure - Instructor (8/26/25 5:22 PM): So my teaching philosophy is your success is my top priority. Uh, we are here, my entire team and I, we're here for you. I focus on your engagement with the material. So that's a fancy way of saying that any minute that you spend thinking about math for me is a success and I try to line up those minutes one after the other. Uh, I prioritize your questions. Grading for me is secondary to learning. We need to have some grading um so that you can honestly assess yourself. Uh, but you will see that my grading in this class is pretty relaxed. Um, I really believe that you are the superstars. Um, and what that also means is that you should also help each other because uh since you're the superstars, you're the most valuable resources that you have for each other. So the more you get to interact with each other, the more you work with each other, the more you listen to each other's questions or answer each other's questions, the more you take advantage of the actual superstars here, which is you. What I admire most in my TAs and also in students is kindness, helping others and patience. Now, one thing that I want to tell you that's important is that I'm neurodivergent. So what neurodivergent means is that my brain is different. My brain operates differently. What I am specifically is HSP autistic. HSP stands for highly sensitive. So that means all sorts of things, but for you specifically, here are some guidelines. Uh, help me help you by knowing that I'm hypersensitive to touch. So I don't like being touched. I don't like touching anybody. I will always fist bump you. Um, that you shouldn't take that personally. That's with everybody. Um, I'm hypersensitive to noise, so that's why I was wearing noise canceling headphones when I came in. I was listening to to background noise so that I I could focus on what I was doing. Um, if you're quiet during lecture, that helps me focus on giving me, giving you the best performance. Now, I hope that my best performance isn't terrible. Um, if it is, then I encourage you not to attend and to just, you know, put the transcript of the recording in GPT to catch up. Finally, I'm hypersensitive to smell, so that's why this classroom has a very stringent no food policy and there's like two signs on every tables and I'm hypersensitive to time pressures. So please be patient with me. I try to always deliver um uh what you want even if it might take a couple weeks or um in the case of people who were not happy with their grades, it might have taken the whole summer, but I always try to come through for all of you. Uh, and then please don't come to my office without an appointment. When I'm grounded, my goal is always to make you happy and fulfilled and to help you on your growth trajectory in the MCIT program. ### Introduction to the course teaching assistants and support resources - Instructor (8/26/25 5:25 PM): So, uh we have a lot of really great teaching um assistance this year, uh all of whom uh have taken this course uh and are or were in the MCIT program. So Dennis and Tiffany um have graduated, but they are still in Philly and you will see them in person. Uh, they're the head TAs and then we have about seven uh really great uh TAs that um you will see on the website when it's released. What to expect from my TAs is that I've handpicked them. Uh, I've taught them. I know I've known them. Um, when I was teaching them, I was thinking, hey, it'd be kind of cool to work with them as a TA. Um, and I feel like you will enjoy working with them. Um, uh, and just take note that they are very different. Um, the TAs are not copy carbons of each other. So, uh if you find some TAs are not your cup of tea, then, you know, maybe try some of the other ones. They've taken this exact course. I've covered that. They're your most reliable source of information. I mean after maybe GPT. No, I didn't say that. Um, and then we'll post office hours at the end of the week. Um, they'll be office hours throughout the week. Um, and recitations will start on Friday uh for this Friday morning. ### Conducting a class survey using Slido - Instructor (8/26/25 5:26 PM): So, before we continue, I I was thinking that we might try out Slido and then give those of you who joined a little bit late an opportunity to scan the QR code. So we're going to do a quick class survey and I'm going to ask just five quick questions and then we'll look at the results together. Okay, so I'm going to launch the survey and I'm going to give you um a minute and a half to complete it. ### Initial discussion on course assignments and expectations - Instructor (8/26/25 5:27 PM): So whenever I give you work, I always put a countdown to make sure that we reallocate that portion of time to you thinking about those questions. ### Managing the completion of the class survey - Instructor (8/26/25 5:29 PM): There's several seats over there. - Instructor (8/26/25 5:29 PM): Okay. Um so that's the time. - Instructor (8/26/25 5:29 PM): I see that um there's been uh 56 votes, 59 and still eight people are typing 10, so I'll I'll give you uh five more seconds. Please try to write up your answer and submit it so that you're not locked out. - Instructor (8/26/25 5:29 PM): Five, four, three, two, one, zero, minus one, minus two. - Instructor (8/26/25 5:29 PM): Okay, I'm going to lock now. Thank you so much. We have 70 votes. That's really great everyone. 71. - Instructor (8/26/25 5:29 PM): Okay, excellent. - Instructor (8/26/25 5:29 PM): So now let's take a look. ### Reviewing the class survey results and student demographics - Instructor (8/26/25 5:30 PM): So, uh, where do you come from? - Instructor (8/26/25 5:30 PM): Okay. So some people are from China. Some people are from Shanghai. Some from Guangjo. So from all over the place. - Instructor (8/26/25 5:30 PM): No, but um it's interesting and um there's some people from Toronto, from Singapore, from Taiwan, from Thailand, from Hong Kong, from Chicago, Maryland, Egypt, Cotswolds in England. - Instructor (8/26/25 5:30 PM): Okay. So that's really um interesting. Now, what was your undergraduate major? - Instructor (8/26/25 5:30 PM): Other. Um, a lot of people did social sciences, humanities, natural sciences, engineering, non CS, fine arts, medicine, computer, law. So I one of them that I forgot is business. Is is that what the other is? Business? Okay, yeah, I should add it next time. - Instructor (8/26/25 5:31 PM): Uh, thank you. Next, the word cloud. What is your current career or job role? - Instructor (8/26/25 5:31 PM): So, student, unemployed, that's normal. Finance, product management, UX designer. So, there's some people already in in CS software engineer. Um, but then there are people in other careers like banking, sales analyst, uh, quant researcher, tax manager. Oh, I I have a problem with back taxes. Can I get some help? - Instructor (8/26/25 5:31 PM): Um, management consulting, uh AI engineer. Oh, already. So graduate student at Penn. Uh, pretty interesting. - Instructor (8/26/25 5:31 PM): So you have a lot of complimentary uh skills. Oh, and one of you is a full-time daughter. - Instructor (8/26/25 5:32 PM): How do you feel about starting the MCIT program? - Instructor (8/26/25 5:32 PM): 4.5, that's pretty great. Um, so I have to say the director of your program Arvind is is one of my favorite colleagues and um what's really amazing about him is that he's been a director for a little bit. Um, I don't know quite exactly how long, but what I've noticed is that every year since I've been here, he's made the management of the program better. So he doesn't think of it as, oh, that's a service role I have to do, but I have all this important stuff I should be doing. No, he really does consider the MCIT his well, to be honest, he considers it his baby and he really, really puts a lot of time into making it better. So don't hesitate to ever give him any feedback. - Instructor (8/26/25 5:32 PM): Next question. How confident are you in your mathematical abilities as you start this course? - Instructor (8/26/25 5:33 PM): Okay, 3.5. So that's pretty good. Um, - Instructor (8/26/25 5:33 PM): So, there's a broad range as you can see. So some of you feel like this stuff is pretty, pretty simple. Maybe some of you will place out. Um, some of you are fairly confident and then some of you have had a few uh bad experiences and that's okay, that's normal. This course isn't going to be hard. This course is going to give you a lot of opportunities to engage with this material. And one of the things I'll tell you is that I'm not one of these people who think that, you know, math is beautiful and it has to be done a specific way and it can't change and if you don't do it that way, then you're a bad mathematician. I feel like math is just a way to put ideas down on your paper, but what's interesting is your ideas. It's a tool to get you where you need to go. So, I'm not going to try to get you to do math in a way that is um impossibly cumbersome if that makes you feel any better. One, twos and threes. - Instructor (8/26/25 5:34 PM): Now, how do you feel about starting the mathematical foundations of computer science course? 4.0. Well, that's pretty good. Um, I I really hope that I'm going to be um uh delivering on that 4.0 and even beyond. So please hold me to it and give me feedback. - Instructor (8/26/25 5:34 PM): What's a fun fact about you? Anonymous or not, you choose. Let's show the participants. - Instructor (8/26/25 5:34 PM): So I'll read through. My dog's name is Base, an alcoholic who's allergic to alcohol. I have two fused teeth. I've represented Asia Pacific team to play baseball at Williamsport. I love sashimi but not sushi. I went traveling for exactly 100 days last summer. By the way, I haven't eaten and I was I wanted to order sushi but I was like, oh, I don't have time and so this is like making me think about that. I feel sleepy now. I used to speak I I hope that's not on account of my lecturing you. I used to speak Hungarian. I hate Boba and the milk tea. I've tried composition, love MMA. You must love politics. Lost both of my shoes when hiking in a mountain. I can fall asleep in one minute. I envy you. I can make art sculptures. I used to keep a journal where I'd write my problems in third person. - Instructor (8/26/25 5:35 PM): I don't that's a very interesting metacognitive tool. I don't break spaghetti in half. Different personalities when speaking Mandarin and English, that's really interesting. Not a big fan of strawberries, but okay with pink drink from Starbucks. I have two cats. I worked as a chess teacher on a gap year. I went to a women college. I like driving. I hope that that's I like driving and I am like driving. I go to the zoo, aquarium for any new place I go to. I love to cook, it calms me down. I've taken classes in a building that I designed. That's neat. I don't like any sauce on chips, um even ketchup. I have orange, I have an orange cat. A distant cousin is the dictator of a South American country. - Instructor (8/26/25 5:36 PM): Maybe that's where we'll do our our end of of year retreat. I play Kendo, board game and fencing. Shy girl. I like shy I am shy girl. I I am born on Christmas. I had consciously eaten a mosquito. I coach trekking. I like travel. I like exploring buildings, learn juggling during COVID, an interesting point. - Instructor (8/26/25 5:36 PM): I love dogs. If that's a well, anyway. I have unpacked and repacked my winter clothes twice during my first week in Philadelphia. I have two dogs back home. I once walked past Conor McDavid in Toronto. I like Led Zeppelin. Been parasailing three three times. Played college hockey. My name means dreams come true in Chinese. That's good to know. I'm 11 years younger than my brother. I've met two US presidents. Do we want to ask which ones? - Instructor (8/26/25 5:37 PM): I'm allergic to chicken. I once ate a Carolina Reaper. I moonlight as a singer songwriter. I failed road tests five times. ### Emphasizing the importance of introductions and networking for student success - Instructor (8/26/25 5:37 PM): Okay, well, I feel like I've gotten to know each other a little bit better. What's really nice is that you're going to get multiple opportunities to do this and uh the next opportunity will be on Friday. So the recitation on Friday, a big component of it is speed networking. And so you should take seriously every opportunity you have to connect with your peers uh because they will help you get a job, they will help you navigate the industry on the other way of these two years. So uh there's no better way to get to know people than now. - Instructor (8/26/25 5:38 PM): Okay. Um thank you so much for uh all these wonderful answers. So now, just so you know, this is what they answered last year. And so well, some things uh were pretty similar. Like most of you were students back then too. But one of the things that's nice is uh uh people seem more excited uh about this course than they were. So I don't know, maybe you all like math a little bit more. - Instructor (8/26/25 5:38 PM): Okay. So I want to really emphasize why we prioritize introductions. I've said it before, but I want to hammer it again. It's the hidden curriculum. It's this is one of the things people never tell you at university or they tell you in some um session at the beginning. The research shows that collaborative learning increases retention by 40%. That means that those of you who manage to get study partners and to study with people will learn more. Now, that research was before uh chat GPT. So maybe if you have conversations with chat GPT, it'll simulate a similar effect because what makes this true is the fact that you're engaging with somebody, that somebody understands 40% of it and you understand 40% of it and you're bringing it together and the fact that you have to explain it to each other and that you're working out through shared difficulties, that's what makes the learning experience better. So that experience of pushing yourself, of critical thinking, of of brainstorming with somebody, um the easiest way is to have it with a human. You can also have it with an AI, but the easiest way is having it with a human. - Instructor (8/26/25 5:39 PM): So, what does that mean? It means that in the first two week, everyone's open to meeting. Everybody is new, it's okay to be awkward, you know, you have a really easy excuse to say, hey, what's your name? But then after week three or four, some social groups start to solidify. It becomes harder to join. If you haven't really yet formed friends, that's when you start, you know, being left on the outside. And I'm telling you, I'm HSP autistic. I'm autistic. I've always been on the outside of social groups. So it sometimes sucks. And then in week eight, you're looking back and everybody's having a fun time and they're in their study groups and they're acing this course and you're all alone. And you'll be wondering, I wish I knew more people in class. And part of it is that, you know, a lot of these classes, a lot of classes in university are very demanding, so you have a lot to do. So some of you are also working to support yourself, so it's really hard to find time. So it's our job to make time in the class for you to meet. So that's why you have introductions. That's why there's sometimes going to be times where you get to talk to your neighbor. Uh take these opportunities seriously because this is really important even though it doesn't get talked about a lot. - Instructor (8/26/25 5:41 PM): So, I'm going to give you multiple opportunities to introduce yourself and I'm going to try to create those opportunities regularly. I'm not going to say I'm perfect, but I know about this stuff and I know that I need to include it in the course. So this is a tacky way of thinking about it, but your degree value is 40% what you know and 60% who you know. Um it's just to indicate that who you know is often more important. And I I have to be very honest. I got this job not by applying on LinkedIn, but because uh I had I was part of a slack community where there were 300 other instructors, some of which were at Penn and I DM them and I asked them how do you like your job and they I said, how do you like your job? And I was like, uh and that's how it started. But the point is I never would have felt comfortable doing that on LinkedIn. I I needed to first make those relationships to be able to then reach out to people. - Instructor (8/26/25 5:42 PM): Okay. So to put this in practice, I want to try to get to know you. So every time you the thing is I'll never get to know you if you don't if I don't learn your name because you'll always be some random floating face of some undiscriminated gender or whatever. And so the first thing you need to do is make sure I learn your name. You need to help me. So every time we have an interaction, just start it by saying, hey, I'm and your name. Or you say, I'm so and so. Uh and you know, I know that I when I remember people and I know that I need to do an effort, but this is also good for everybody else in your life. So when you meet somebody, just introduce yourself. Just assume they don't remember your name and just say, hey, I'm so and so. And if they say, yeah, I know, that'll make your day, right? Because they'll remember you. But just get in the habit that most people don't introduce themselves enough and that's how you never remember people's names. ### Discussing the foundational purpose and relevance of the course - Instructor (8/26/25 5:43 PM): So, okay, enough about this stuff. Um, why this course? - Instructor (8/26/25 5:43 PM): So the big picture is that this is the foundation for a bunch of other courses including CIT 5960 or CIS 5020, which by the way, I'm signed up to teach next semester and that's going to be exciting. - Instructor (8/26/25 5:43 PM): So those are so that's the big picture. It's a requirement for other courses. So you need to know this material for other courses. But the real reasons are, it's going to start helping you develop your formal computational thinking. Uh, it's going to enable you to be more precise in your technical communication, no matter what kind of job you end up having. And hopefully, um, it will build confidence for your independent learning of other technical skills like maybe machine learning. ### Instructor's philosophy on course evaluations and feedback - Instructor (8/26/25 5:44 PM): So first I'd like to, if you read the course, I I just recreated these slides. I usually have a slide about course evaluations, but I take course evaluations very seriously. Some of my colleagues, you know, think, oh, students are mean, you know, they say mean things about me, blah, blah, blah. I consider that, you know, you're so busy that those of you who've taken the time to write any number of words in those damn forms, you know, that I really appreciate it. Um, I also know that students come from various different horizons. You know, you've had different conditions in the course, so any feedback on it is really exciting. - Instructor (8/26/25 5:45 PM): Last year, I unfortunately my father had a really bad health emergency. He, I thought he was going to die. They thought he was going to die. So I I took time off and the good news is that he didn't die, but I had to spend a month and a half there. Um, and uh it it was it was a good experience for me and my father, but less so for uh the students. I'm fortunate that Arvin was able to step in, but of course, you can understand that having multiple instructors and they created a lot of chaos and that's reflected in the course evaluations. - Instructor (8/26/25 5:45 PM): Um, but other than that, I read these course evaluations. I've made numerous improvements. Um, for instance, the course website was introduced last year based on course evaluations. And I don't want to wait until the end of the year to get your feedback. So at the end of every lecture, you will get three questions on Slido, um, to ask you for your feedback and I read it that evening when I'm commuting back home. I have an hour and a half to New Jersey, so there's time to keep busy. - Instructor (8/26/25 5:46 PM): And the reason I want to read you this evaluation is not because it's flattering, but because this student was able to capture what I'm trying to do. So, the best math professor ever. I grew up taking math courses, but he's the only teacher who really made me learn something. He not only taught us math, he taught us the way to think about things, which is far more important than the concepts per se. He was always sincere. Some other math teachers like to impress. They learned things by heart themselves and they talked as if they know everything since they were born. Jeremy is different. He paused to ponder over things and he pointed out the ambiguity and the questions people may have. He is able to be vulnerable himself, which makes him super strong. I must say I got more than I expected from this course. Love you, Jeremy. I'm sure 5920 will be popular since now because of you. - Instructor (8/26/25 5:47 PM): Well, that's flattering, of course, but the main thing that I really appreciate about this review is that what I'm trying to show you, I'm not trying to impress you. I will make mistakes. So the main way I lecture is through a tablet. I run through examples. And what I'm trying to do is I'm trying to walk you through how I'm thinking things through if I were just thinking them through like you as a student, not as an expert. Um, I'm trying to show you when I don't remember something, how I try to figure it out. When I make a mistake, how I catch myself up. All of those are metacognitive skills and actually, when you're actually working, they're the most important skills because nothing, news flash, nothing works out the way you intend in life. So you always have to figure out, you know, how are you pivoting, how are you figuring that next problem out. And so that's what we're going to try to do in this course. That's what I hope to be doing in this course with you. ## Course Content, Methodology, and Applications ### Detailed breakdown of course material and teaching methodology - Instructor (8/26/25 5:48 PM): So, uh one link I will provide on the website, uh when it's released at the end of the week is a link to this form on Amazon. It's this big plastified form and these are the two sides of them. And the reason I show you this form is because it's a compendium of everything we're going to cover in this class. - Instructor (8/26/25 5:48 PM): Like literally, everything we're covering in this class is in those two pages. Yeah, that's it. So we're not going to cover a lot of material. Those are all of the definitions and what we're going to be doing in this course is practicing those definitions. We're going to be looking at examples of those definitions. We're going to be looking at proof of those properties. We're going to see how everything connects to each other, but the material itself is really simple, it's really small, there's not that much to it. The reason I'm saying that is because this is a course where you have to, like right now is the only time I'm going to have slides at. The rest of the time, I'm going to have a tablet. I expect you like these gentlemen here to have a tablet and to write and to think with me on all of these examples that we're covering. - Instructor (8/26/25 5:49 PM): If you don't do that, there's there's no material. You could just buy this, go home and be done with it. So what we're creating this in this class is an opportunity to practice. The material is everywhere and there's not that much of it. - Instructor (8/26/25 5:49 PM): Now, here's the way that we'll cover it. I like to to say it this way. Part one, I introduce the characters, the objects. So who are they? There's sets, there's functions, there's relations, there's permutations, there's combinations, there's probability and expectations. Those are like the characters of a story. Now, part two is the actual story. What is it? The story are the proofs. It's how we tie together all of the characters using propositional logic, proof methods and mathematical inductions and we connect all those objects to put them all together into what I call a story. So, in the first part of this course, you're learning about the characters, but it will feel like we're just saying, here's one character, here's another character, here's another character and it will feel very disconnected. That makes sense because it's only in part two that we'll actually do something with those characters. And then once we've done that with the simple concepts, we'll start part three where we'll do both at the same time and I'll introduce graphs which are one of the most fertile concepts in computer science, right? Because everything is a graph in computer science, internet and all of that. ### Addressing student questions and transitioning to applications - Instructor (8/26/25 5:50 PM): So I see um that are that there are three questions. So now's a good uh time to pause before we go into discussing applications. First, I'd like to thank um the people who uh ask those three questions. Advice on how to uh form study groups. - Instructor (8/26/25 5:51 PM): To be very honest, um I I'm not sure that I have advice on how to form study groups because where I'm thinking right now is should instructors mandate study groups. And I'm wondering whether I should just randomize all of you and say, you know, you're in study group one, you're in study group two, and study group three. - Instructor (8/26/25 5:51 PM): The problem is that as a neurodivergent person, I've the rules have always, you know, have always uh been miserable for me. So I've always really valued my ability to choose because nobody really knows what I need because I'm so different. - Instructor (8/26/25 5:52 PM): So, I find it very hard to force students to do things or to force students into pairings that are random, for instance. Now, the reason I am saying that is because I I really think that instructors need to do more because it's really hard to form good study groups. So, - Instructor (8/26/25 5:52 PM): My advice is uh here's what I will say for MCIT. So this is not advice for everybody. MCIT is a program, especially with with Arvind, um and we just recruited a new administrator, Julia Hawthorne, that's dedicated to this program. - Instructor (8/26/25 5:52 PM): There is a number of people that are here to organize events and so there's like um there's going to be I think a hackathon. Uh there's going to be a lot of of social events that are organized for you. Attend those events. Uh maybe put a name tag. Uh make sure to talk to a different number of people, you know. So maybe, you know, we can all make an agreement that at these events, you're never going to talk more than 10 minutes to the same person. - Instructor (8/26/25 5:52 PM): And then once you've spoken 10 minutes to somebody, snap to somebody else because you don't have that many of those events. If once you've met one person you like, you just spend the whole event with that person, then you're only come out of that event having met one person. - Instructor (8/26/25 5:53 PM): Now, some of us like making deeper connections, so maybe 10 minutes is too quick for you. So maybe say, I'll meet three people. I'll spend like half an hour with each one of them. But try to make an effort to to rotate and do show up to these events. It's not because of the free food, uh it's because it's it's an opportunity to gather with other people. - Instructor (8/26/25 5:53 PM): Uh the second thing I'll say is that if if really um one of the things I can suggest is we can try to create a spreadsheet or uh where uh those of you who want help um being matched for study group can submit a form and then I'll pair you randomly. - Instructor (8/26/25 5:53 PM): So if I were to do that, um I'll take a survey to see if there's interest. If I were to do that, I would match you on availability and working style. So availability is when are you free in the week and working style is do you do things early or do you thing do things last minute because that's usually where people kill each other. ### Clarifying Course Website and Canvas Access, including the Waiver Exam - Instructor (8/26/25 5:54 PM): I hope that was helpful. You mean, thank you for the question. When you say website, do you mean the canvas, the page on canvas? No, so I I I created the canvas, but I may not have published. Do you have access to the canvas? - Instructor (8/26/25 5:54 PM): Yes, several days ago. Several days ago. CS was alive, but now it's. - Instructor (8/26/25 5:54 PM): Okay. Yeah, yeah. So, but the canvas, is it? - Instructor (8/26/25 5:54 PM): No, alive. - Instructor (8/26/25 5:54 PM): Okay, so I forgot to click the publish button on canvas, so I'll do that. But there's a separate website. It's math for CS, but I haven't updated it for this term. Um, there's no secret. If you want to go to last year's, you just type fall 24.mathforcs.edu. - Instructor (8/26/25 5:54 PM): Um, but the website will be ready soon. So there so to answer this question, there's a separate website and it's on that website that the waiver exam will be. The waiver exam is entirely online. Is there also see uh that I don't know. I'm I'm sorry. I will be teaching it in the spring, but I I don't know over the summer. They hire right before. ### The Utility of Learning LaTeX for the Course and Beyond - Instructor (8/26/25 5:55 PM): How useful is it to learn Latech for this course and in general? It's uh one of the goals of this course is to learn Latech. Now, I want to be really transparent with you. I don't know how valuable it is to learn Latech because of LLMs, because of all sorts of reasons, but I know that um the other courses still use Latech, still require Latech and they still consider that I'm supposed to be teaching it to you. So we're going to all be learning Latech together. ### Demonstrating Real-World Applications of Discrete Mathematics in Computer Science and AI - Instructor (8/26/25 5:55 PM): Thank you so much for these questions. Uh we'll have ample time to take more. Um now I'm just going to dive into uh some of the applications. Um so you all came here uh because you were doing something else and now you want to do computer science. So I can understand if you think of this course is like, uh, you know, like you told us we were coming to do computer science and then there's this random course with unrelated topics. - Instructor (8/26/25 5:56 PM): So I really do want to convince you that this is really connected. This is really um a skill set that is important in computer science and in AI. So one real world application of discrete math, sets. Sets are the first objects we're we're going to cover. So where are sets involved? Well, in database operations. - Instructor (8/26/25 5:56 PM): Almost every part of structured data that you ever encounter, like your septic keys, like your student information, like your bank information, all of that is all stored in databases. And there's a small number of database technologies and one of them is the SQL, SQL. SQL. And the SQL uh database system has a query language that looks like this where you select parts of a larger set. - Instructor (8/26/25 5:57 PM): So all of the formalism, the language, the theory behind that and the ability to formulate queries in that language comes from set theory, which we are covering in the first chapter of this course. This is not just database queries, but it's also the basic algebras to filter data in any data pipeline. - Instructor (8/26/25 5:57 PM): So for instance, if you've ever written Python, um you at some point might have filter lists where you select elements in a list and those comprehensions are set operations. So another obvious one, logic. Uh so we're going to cover logic in this course and logic is is involved in a large number of of applications, but here are a couple: simplifying code and digital circuits. - Instructor (8/26/25 5:57 PM): So logical reasoning helps you simplify complex conditional statements. So if you have a whole bunch of nested ifs, you can figure out how to combine them into a simple structure and to debug programs systematically. If this is like this and this is like that, then this is the outcome that I should have and if not, then there's a problem that I can catch here. - Instructor (8/26/25 5:58 PM): So every time that we do debugging, we're using deductive reasoning, which is derived from logic. So an example is all MCIT students implies looking for new jobs. So you're an MCIT and therefore we'll help you with job search. So those are two logical implications. - Instructor (8/26/25 5:58 PM): Another real world applications of proofs, writing bug free code. So the ability to write proofs means that you are able to write programs with few bugs. Uh so it both requires translating your thoughts into unambiguous expressions and it's essential for critical systems, so medical device or aviation. Um it's also proof writing is also the foundation for algorithm analysis. - Instructor (8/26/25 5:59 PM): You'll probably see this quote many, many times by Donald Knuth, who was one of the uh fathers of um analysis of algorithms. So he wrote books called the Art of Computer Programming and he says, beware of bugs in the above code. I have only proved it correct, not tried it. - Instructor (8/26/25 5:59 PM): So what he was saying is that proving code and testing it are two complementary things that we must do for programs. ### General Benefits of Discrete Mathematics: Clarity, Efficiency, and Relevance with AI - Instructor (8/26/25 5:59 PM): But another uh real world application is just the discrete math itself. It will make you clearer uh because you will be able to uh describe abstract problems with notation. - Instructor (8/26/25 5:59 PM): You'll be able to generalize problems and you'll be able to parameterize problems. Um, so instead of saying, oh, um, I'm going to roll a dice uh with six face, you might end up saying I'm going to roll a dice with N face and N could be any number between one and whatever infinity. - Instructor (8/26/25 6:00 PM): It will make you faster. Uh these definitions build on each other and are recursive. So once you've understood a small number of them, it makes you understand um the rest much more easily. Um, and understanding this will help you understand more complex and often more efficient algorithms. - Instructor (8/26/25 6:00 PM): So in particular, now every algorithm is often implemented in a library, often um the libraries are even selected by um LLMs. - Instructor (8/26/25 6:00 PM): But I use LLMs to code a lot. I do a lot of vibe coding and every shade in between that. Uh and I can tell you these LLMs, even though they're magical, they still need you to exercise judgment. And the more you need to exercise judgment, the more you need formal reasoning skills as opposed to just being able to write lines of code. - Instructor (8/26/25 6:01 PM): So the value of of this is is even broader now that we have um assistance uh like Claude and Chat GPT. ### Illustrating the Need for Formal Specification with Real-World Examples - Instructor (8/26/25 6:01 PM): So I want to give you a really concrete explanation instead of just hand waving my my hands about formalism and all of that. - Instructor (8/26/25 6:01 PM): So my first example is uh the the $10,000 bug, you know, what if your boss told you to sort the customer records by date? What would that mean? - Instructor (8/26/25 6:01 PM): Well, it could be anything. So here's five different ways you could have done it differently. So developer A decided that that meant sort the customer records by the date that the record was created. - Instructor (8/26/25 6:01 PM): Developer B, that's a reasonable assumption. Developer B was said, okay, well, created, but sometimes you might modify it and then you want that one to be back on top. So sort it by date modified. - Instructor (8/26/25 6:02 PM): Developer C was like sorted customer records by date of of of birth. So pick just some random date. - Instructor (8/26/25 6:02 PM): Um, developer D uh picked any one of those but sorted newest to oldest. Developer E sorted oldest to newest. So there's five different implementations, there's angry customers and there's weeks of rework. - Instructor (8/26/25 6:02 PM): And by the way, you know, that idea that in computer science we need to be a little bit more formal and also trace back to this meme that you might have seen, uh which is more used in software engineering for product design, but it's the same idea. - Instructor (8/26/25 6:02 PM): Now, if instead of saying sort the customer records by date, you're given a mathematical specification, then this is air tight. This there's no ambiguity what this is. Uh this is a very precise specification of one kind of sort. - Instructor (8/26/25 6:02 PM): Now, here's another example. Uh say that you're at a company and your manager tells you to build like a platform and says, oh, it should be fast. Well, what does that mean? Does that mean fast response time? Uh does it mean that it should be able to handle many users? Uh and so for each of these types of requirements, those requirements are very ambiguous. - Instructor (8/26/25 6:03 PM): So instead when we use math, when we use precise quantifications, it looks like something like response time in the 95th percentile less than 200 milliseconds or throughput allows more than 10,000 requests per second without choking. - Instructor (8/26/25 6:03 PM): Or availability is available more than 99.99% of the time. Even better, if you are comparing algorithms, you would be using the big O notation. So instead of saying the search algorithm should be efficient, you would say the search algorithm should use O leg log in time. So what does that mean? - Instructor (8/26/25 6:04 PM): Now, if you say that the time complexity of your algorithm is log n, you know that if you double the data size, you're only adding about one operation. - Instructor (8/26/25 6:04 PM): So you know that for 1 billion items, you're only need on order of 30 operations. Maybe it's K30, but it's still a factor of 30. So that's that's very impressive because it means that you'll be able to double the data load much more than if it were a linear algorithm. - Instructor (8/26/25 6:04 PM): So we can make precise architectural decisions and these are decisions that again, um the LLM is not always able to make because the LLM doesn't always know what is going to scale if you don't tell them. ### Applications of Counting and Probability - Instructor (8/26/25 6:04 PM): Some more applications, uh counting and probability. Uh so this is used absolutely everywhere. Uh here are a couple examples, performance analysis. How long will my program take or how long will my battery last? Those are the two facts of the same problem. Scalability, how does runtime grow with data? - Instructor (8/26/25 6:05 PM): Machine learning, uh the core of ML algorithms is Bayesian and Markovian and all of that. Randomized algorithms, expected runtime analysis. Financial systems, risk assessment. What's the likelihood that this person will default on their debt. ### Applications of Graph Theory - Instructor (8/26/25 6:05 PM): Real world applications of graph theory. So graph theory, uh the applications are prodigious. Um Google's page rank algorithm, the algorithm that uh creates a score uh based on the does uh please raise your hand who's heard of the page rank algorithm. - Instructor (8/26/25 6:05 PM): Okay, good. So, um GPS and maps. So that's the shortest path algorithm. The map is a graph and when you're trying to get to a place, the map is computing the shortest path algorithm, which you'll see in the algorithms course. - Instructor (8/26/25 6:06 PM): Social networks, friend recommendation, that is also an example of graph theory. Internet routing, when you are requesting a a web page, um the internet network is very dense. So between any two points, there's many different ways to go. And so the router network is trying to figure out what is the most efficient path to get you your data, your Netflix uh streaming for instance. - Instructor (8/26/25 6:06 PM): Recommendation systems often use user item graphs to establish correlations between different clusters of users. ### Course Resources and Q&A on Applications - Instructor (8/26/25 6:06 PM): So, having covered all of those um applications, here are the resources that we're going to be using in this course. So, - Instructor (8/26/25 6:07 PM): So wait, at this moment for the applications, let me just pause to ask if there are any questions on these applications. - Instructor (8/26/25 6:07 PM): Are you sufficiently convinced that this is actually a an NCIT course that it actually is meaningful to have this here? - Instructor (8/26/25 6:07 PM): Good. - Instructor (8/26/25 6:07 PM): Okay. - Instructor (8/26/25 6:07 PM): Any questions? - Instructor (8/26/25 6:07 PM): Yes. - Unknown (8/26/25 6:07 PM): From which Wednesday? - Instructor (8/26/25 6:07 PM): The website that's going to be out at the end of the week. - Unknown (8/26/25 6:07 PM): Oh, okay. - Instructor (8/26/25 6:07 PM): I I probably will uh so um this is the only course where there will be slides. I will be every doing um tablets and I will post a PDF of the tablet after the course. - Instructor (8/26/25 6:07 PM): Yeah. - Instructor (8/26/25 6:07 PM): Thank you for the question. - Instructor (8/26/25 6:08 PM): Okay. ### Overview of Course Platforms and General Resources - Instructor (8/26/25 6:08 PM): So the course resources, um uh the website will be at uh math for cs.university. Uh I'm uh transitioning it to this new term, so for the moment there's a placeholder. - Instructor (8/26/25 6:08 PM): Uh for the discussion forum, uh we will be uh uh looking at Ed discussion. - Instructor (8/26/25 6:08 PM): Uh we will um have a grade scope and prairie learn as homework platforms. - Instructor (8/26/25 6:08 PM): Uh for Latech writing, um we recommend you use Overleaf. - Instructor (8/26/25 6:09 PM): There's a a large number of textbooks. I I will post a blog post where I've reviewed a number of options. - Instructor (8/26/25 6:09 PM): But there's there's like I want to say seven to eight textbooks. Um I'm going to take out of a few of these textbooks, uh but you can study with a textbook of your own. - Instructor (8/26/25 6:09 PM): Uh there's a couple resources that are free. There's the online lecture notes uh by Arvin. So they will be available on the website, but another resource that you might be interested in is uh our GitHub organization. - Instructor (8/26/25 6:09 PM): So that's github.com/cit-5920. ### Recommended Textbooks and Lecture Notes Repository - Instructor (8/26/25 6:09 PM): Okay, and so there's um a repo called lecture notes and it has all of the the lecture notes. Um so you can download either the chapters individually or you can download the whole thing. - Instructor (8/26/25 6:10 PM): And so I I I still follow pretty much the same exact progression and I cover the same exact material. - Instructor (8/26/25 6:10 PM): Um so one of the things I I encourage you to do and I encourage you to do it uh so we'll talk more about this. So we'll come back to this uh later. - Instructor (8/26/25 6:10 PM): Uh feel free to report any mistakes uh that you see or any corrections here. - Instructor (8/26/25 6:10 PM): Uh and then the other uh textbook that I recommend is a cool brisk walk through discrete math. So that's a free textbook. - Instructor (8/26/25 6:10 PM): It's completely free. You can download it, you can do whatever you want with it. Um what what I really like about so it covers um I'll link to it in um the website. - Instructor (8/26/25 6:11 PM): It covers uh almost our entire uh curriculum in this course and it's very accessible. It's uh it talks to you as opposed to just giving you a bunch of definitions. - Instructor (8/26/25 6:11 PM): I think that sometimes he's a little bit um he simplifies some things a little bit too much, but overall he's I think one of the best textbooks out there uh for this course. - Instructor (8/26/25 6:11 PM): Uh and and um we will add more uh resources on the website, but um you can you can look at the repositories here. - Instructor (8/26/25 6:11 PM): So I'll post all of this on the website, but you can already access it. There's three documents here. ### Supplemental Documents for Foundational Concepts and Common Errors - Instructor (8/26/25 6:11 PM): One of them is um the algebraic simplification rules. So uh this is a document to uh recap. These are prerequisites. - Instructor (8/26/25 6:12 PM): It shows you all of the kinds of rules that I assume you know or at least that I'm not going to reteach um so distributive property, multiplying powers, dividing powers with the same base, power of a power, zero exponent rule, negative exponent rule, factorization. - Instructor (8/26/25 6:13 PM): So we'll we'll mention these documents in the assignments when uh looking them up might be useful if you're lost and there are practice exercises. None of them are are graded. - Instructor (8/26/25 6:13 PM): Um there's a discrete math lexicon. Uh so this is a table where um there's um each of these words is in every different language. So um this is the term in English, this is the version in French, in Spanish, in Chinese, and then a definition, an example, a Wikipedia link. And so this covers all of the concepts uh in the course. If you ever want to do flash cards or if you want to um throw this into uh GPT to ask for like study questions of some sort. These are the concepts we're covering in the course. - Instructor (8/26/25 6:14 PM): Uh next is uh the common mistakes primer. So this is just a list of common mistakes that uh uh people make on the algebraic stuff. So for instance, 4x means 4 * x. It doesn't mean 4 + x. - Instructor (8/26/25 6:14 PM): Uh so that might sound silly to you, but these are common misconception. If you have x * x * x, it's x cube, it's not 3 * x. Um the order of operation is parentheses, brackets and exponents, orders, multiplication and division from left to right. - Instructor (8/26/25 6:14 PM): and so on and so forth. - Instructor (8/26/25 6:15 PM): So these are sort of like I'm trying to make sure that if there's um so this we will wait. ## Course Policies, Logistics, Support, and Waiver Exam ### Teaching Approach and Engagement Strategy - Instructor (8/26/25 6:15 PM): Active approach would be, and I'd be open to you if that's what you all wanna do. - Instructor (8/26/25 6:15 PM): In a fully active approach, I assign you readings, and then you come here, questions and you answer them and we discuss what you've read. - Instructor (8/26/25 6:15 PM): Over time, I found out that everybody is so busy that it's very hard to get everybody to show up having read the reading. - Instructor (8/26/25 6:15 PM): And so then you have half the class who's read the reading, half the class who hasn't, and you don't know if you should go over it again or if you should leave half the class in the dust. - Unknown (8/26/25 6:15 PM): And so it's an experience that makes everybody unhappy. - Instructor (8/26/25 6:15 PM): So what I try to do instead is I try to lecture a little bit, then put some quizzes, not in this lecture because it's mostly intro, and to do a lot of engagement in the class. ### Overview of Homeworks and Recitations - Instructor (8/26/25 6:16 PM): Now, in homeworks, there will be two types of homeworks. - Instructor (8/26/25 6:16 PM): There will be the online portions, and all of those will be done on something called Prairie Learn. - Instructor (8/26/25 6:16 PM): So Prairie Learn is a platform where you will get a lot of questions, And all of those questions are randomized. - Instructor (8/26/25 6:16 PM): So you can try them any number of times. - Instructor (8/26/25 6:16 PM): So for instance, if you have a question that teaches you how to add two numbers, you'll get two plus five. - Instructor (8/26/25 6:16 PM): And then if you get that one wrong, you'll get seven plus three, and then if you get that one wrong, you'll get 11 plus two, and so on and so forth, until you get it right. - Instructor (8/26/25 6:16 PM): And so in the online exercises, the goal is to try to get the answer right on a consistent basis. - Instructor (8/26/25 6:16 PM): So if you get it right once, that's great, but the goal is to get as many points as possible. - Instructor (8/26/25 6:16 PM): So if you get it right multiple times in a row, you can accrue a lot of points. - Instructor (8/26/25 6:17 PM): So Prairie Learn is entirely about practicing, trying to make sure that you understand, and trying to build what is called your mastery. - Instructor (8/26/25 6:17 PM): Once you've built your mastery, the written portion is are are more critical thinking. - Instructor (8/26/25 6:17 PM): They are are a little bit more theoretical, and they will require that you practice different skill sets. - Instructor (8/26/25 6:17 PM): So instead of just knowledge, it will be reasoning and comparing and contrasting and synthesizing. - Instructor (8/26/25 6:17 PM): The recitation will be practiced for the written problems. - Instructor (8/26/25 6:17 PM): So there will be hands on problems and TAs I'm sure you've already been into recitations like that, but we'll give you ten minutes to think, and and then they will grade the answer, and then they'll give you a little bit more to think, and then we'll discuss the answer and so forth. - Instructor (8/26/25 6:17 PM): It's necessary practice. - Instructor (8/26/25 6:17 PM): If you find it terrible, just give me feedback so I can tell them to change the format. - Instructor (8/26/25 6:18 PM): The thing I want to highlight is really, Prairie Learn is is one of the best tools because you get to practice, over and over and build mastery before you actually try to engage in these concepts. ### Grading Breakdown and Exam Weighting - Instructor (8/26/25 6:18 PM): Now the grading distribution is the weekly homeworks will be worth 45% of the grade. - Instructor (8/26/25 6:18 PM): There'll be three exams, and they'll be worth 45% of the grade. - Instructor (8/26/25 6:18 PM): 5% will be dedicated to professionalism. - Instructor (8/26/25 6:18 PM): That means the way you treat TAs, the way you treat other peers, the way you treat me. - Instructor (8/26/25 6:18 PM): Don't be aggressive. - Instructor (8/26/25 6:18 PM): And then engagement, giving feedback, asking good questions. - Instructor (8/26/25 6:18 PM): Those are both five percents are are things that I will assign at my discretion. - Instructor (8/26/25 6:18 PM): For exam waiting, we will be waiting the best exam, 17%, the second best exam, 15%, and the third 13%. - Instructor (8/26/25 6:19 PM): The first exam and the second exam are on different parts of the course. - Instructor (8/26/25 6:19 PM): The final exam is cumulative, so it covers the entire course. - Instructor (8/26/25 6:19 PM): But even though it's it's cumulative, if if it's the one you you messed up the most, it will be weighted 13%. - Instructor (8/26/25 6:19 PM): So the bottom line is we try to minimize grading stress so you can focus on learning. - Instructor (8/26/25 6:19 PM): The goal is really that you try to, you know, keep yourself motivated learning these concepts so that they're ready for the next class. ### Letter Grade Assignment and Course Performance Trends - Instructor (8/26/25 6:19 PM): There's a there's a question on how letters grades are assigned. - Instructor (8/26/25 6:19 PM): So the the course is not curved, so I don't have a fixed set. - Instructor (8/26/25 6:19 PM): I just have I have thresholds that I don't disclose, but I if everybody in this class has an a, you know, we'll all be the happiest. - Instructor (8/26/25 6:20 PM): And in past years, the the distribution of the class was a, a minuses. - Instructor (8/26/25 6:20 PM): There were a few a pluses and then some b's. - Instructor (8/26/25 6:20 PM): And the only student who has failed the class has since gotten a passing grade. - Instructor (8/26/25 6:20 PM): And one student has an incomplete and will get a passing grade soon. - Instructor (8/26/25 6:20 PM): So, no stress on your grade. ### Key Course Policies: Collaboration, AI, and Extensions - Instructor (8/26/25 6:20 PM): Key policies overview. - Instructor (8/26/25 6:20 PM): So for collaboration, work with one partner allowed. - Instructor (8/26/25 6:20 PM): So you must write your own solutions and you can change partners. - Instructor (8/26/25 6:20 PM): So this doesn't mean that you can't study as a group. - Instructor (8/26/25 6:20 PM): It just means that when you're working on actually writing up the assignments, you should be working with one partner. - Instructor (8/26/25 6:21 PM): Why do why have this policy? - Instructor (8/26/25 6:21 PM): Because when groups get too large, it's not always clear how much work each person did, and it's not so much that that I wanna force you to do all of this work, but it's just even if you were had the best of intentions, it's not clear for yourself whether you've done all the work that's necessary. - Instructor (8/26/25 6:21 PM): So for AI usage, I I have another slide on this, but AI is, of course, used as an assistant. - Instructor (8/26/25 6:21 PM): I recommend urge that you get a paid subscription, and you must understand that everything you submit, you must understand it. - Instructor (8/26/25 6:21 PM): For extensions, we have a no time pressure policy. - Instructor (8/26/25 6:21 PM): So just please request on the website, there will be an extension form request. - Instructor (8/26/25 6:21 PM): Just submit an extension request if you need an extension, and it will be approved as long as it's submitted before the deadline has passed. - Instructor (8/26/25 6:22 PM): So what that means is that if you submit an extension at Monday, '11 fifty nine for the deadline that's at midnight, that's fine. - Instructor (8/26/25 6:22 PM): The point here, it's not that these all these deadlines, why do we have deadlines? - Instructor (8/26/25 6:22 PM): We have deadlines so that graders can grade a workload and we can move on with our lives, so we can release solutions and all of that. - Instructor (8/26/25 6:22 PM): But the main reason that I have this form is because what's important for you is to organize your time. - Instructor (8/26/25 6:22 PM): You know? - Instructor (8/26/25 6:22 PM): If you are struggling to organize your time, I want to be able to distinguish that from somebody who's just overwhelmed and knows that they need more time and will get to it at some point. ### In-Depth Discussion on AI Tool Recommendations - Instructor (8/26/25 6:22 PM): Okay. - Instructor (8/26/25 6:22 PM): So I want to talk a little bit about AI. - Instructor (8/26/25 6:22 PM): So I'm a I'm very much pro AI. - Instructor (8/26/25 6:22 PM): I've been encouraging my students to use it in my courses for a year and more. - Instructor (8/26/25 6:23 PM): But the thing that I really would request is that you get a paid subscription. - Instructor (8/26/25 6:23 PM): It's not enough. - Instructor (8/26/25 6:23 PM): DeepSeq is excellent. - Instructor (8/26/25 6:23 PM): It's really, really, really good, but you need to get a paid service. - Instructor (8/26/25 6:23 PM): So pay for ChatGPT or pay for Cloud. - Instructor (8/26/25 6:23 PM): Those are that's my advice. - Instructor (8/26/25 6:23 PM): I have both. - Instructor (8/26/25 6:23 PM): I was telling my students that just to give you an example, I have ChatGPT Pro. - Instructor (8/26/25 6:23 PM): I have Cloud Max. - Instructor (8/26/25 6:23 PM): I have perplexity pro, not the perplexity max because perplexity is not good, but I have all three of those services and more, and I use them all of the time. Um, in every way, in every uh project, uh I code a lot with these tools and so these tools are not going to replace you, but people who know how to use them will if you don't get on the bandwagon. So my advice is get a paid subscription. It's the best investment you will ever make. ### Understanding the Purpose of Education and Learning - Instructor (8/26/25 6:24 PM): So then learn to differentiate between learning and unlearning. It's really important. So one of the really important things is that it's really important to understand that pleasing the professor is not at all important. I get paid, uh, I have the privilege of getting paid to teach you, which is something I really love. Um, I try to do the best that I can, but I have limitations. At the end of the day, you come here to learn something, and if the only thing that you're doing is trying to submit whatever will get you a good grade, you're missing out on your time and I'll talk about this again, your time and your money and your opportunity cost. - Instructor (8/26/25 6:24 PM): So it's really important that you understand when you are using these tools to make me happy as opposed to using these tools to get the answer that you deserve. If you're using these tools to pretend like you're understanding this, uh, I feel bad because I'm getting paid off of your suffering, off of the fact that you're not getting any smarter, but I'm still getting paid to teach you. ### Practical Strategies for Engaging with AI Tools - Instructor (8/26/25 6:25 PM): The third thing is always think critically. So the worst way to interact with these agents is giving them something, taking the answer. It's like a one and done. It's like a wham bam and thank you ma'am. So don't do that. What's really wonderful about these agents is the opportunity to engage with them. Particularly when you're not using the coding agents like Claude code or Windsor for cursor, but when you're you're interacting with the agents as chatbots, it's really great to engage in conversation. So even if you are asking for the solution of a problem, then ask, why did you do it this way? Uh, could you do it some other way? Could you explain me the step? Could you give me some other related example? - Instructor (8/26/25 6:26 PM): Think critically, make sure that you are engaging with the agent to make sure that you're double checking your understanding. - Instructor (8/26/25 6:26 PM): So here are some practical tips. I have lots of them because I use these all the time, but um, these lectures are going to be recorded, the videos are going to be posted on the website. Uh maybe they're they'll be even accessible on canvas and the transcript is available. So just put the transcript and GPT and say, you know, what the heck was Professor Lumbroso talking about today? - Instructor (8/26/25 6:26 PM): Uh, or I didn't get that that thing he was talking about the thing magic, could you reexplain it? You have access to the entire transcript and chat GPT can explain it uh for you. Um, another thing is one of the best uh ways to use chat GPT is by asking for examples, by asking for analogies, by asking for metaphors, uh by connecting these examples to things that you're interested in. So one of the first assignments that you will have is to create like some text document with your interests and the things that you care about. And we're going to be using that in context engineering to get examples that are compelling to you from um this math material. - Instructor (8/26/25 6:27 PM): Another thing that I would would encourage you to do is, you know, be creative like you can combine multiple sources of information. So for instance, you could put the the lecture notes for chapter one uh on Thursday, you could put those lecture notes and my transcript to try to have GPT align uh what was in the lecture notes and what I was saying, you know, compliment, give me the combined information from these two sources of information. - Instructor (8/26/25 6:27 PM): And then the other thing that I would really really heartily recommend is um, don't just use the dictation of these subscriptions, but there's this tool called Super Whisper. Um, will this work? Yeah. So here I am dictating and Super Whisper will enter it into the URL bar. - Instructor (8/26/25 6:28 PM): So I use that all the time. So all of the time I'm talking to Chat GPT, I'm talking to Claude because the time that you take to go from an idea that's in your brain to writing it down is painful. You can go four times faster if you speak directly uh as your mode of input. So I speak all of the time. - Instructor (8/26/25 6:28 PM): Okay. ### Emphasizing Academic Integrity and the Value of University Education - Instructor (8/26/25 6:28 PM): So I see there are a few questions. I'm I only have a few more slides, so I'm going to go through them and then I'll take all questions at the end. So now that I've spoken about Chat GPT and all of that, I want to talk about academic integrity. So I've already mentioned this, but I want to mention this again and even write it on the on the slide. This is your education. This is your money, this is your time, and this is your opportunity. If you weren't spending this money, you could be spending it on something else. If you weren't spending time here, you could be doing so much else. You could be starting a business. You could be uh following some really rich person and and and growing into their sphere of influence. Like there's millions of things that you could be doing but sitting in this classroom and submitting uh dishonest homework. - Instructor (8/26/25 6:29 PM): I know that some of you do not believe this, but your university diploma is more than just a piece of paper. Um, I know that some of you think that universities are corrupt and that the only point of a university is to get this piece of paper, that piece of paper that will get you the jobs that you want. But I really believe that that's not what university is about. We really try to to teach something useful. That doesn't mean we always get it right, but we really try and you need to really try as well for it to even have a chance of working. - Instructor (8/26/25 6:30 PM): So one of the reasons why I love teaching uh CIT 5920 is because I get to teach the MCIT and because you've already been for a lot of you, not all of you, but for a lot of you've already been in the job market. Um, a lot of you are a lot more mature learners. It's one of the greatest pleasures of teaching the MCIT students. It's why uh instructors don't rotate out of these courses usually. - Instructor (8/26/25 6:30 PM): If you're not interested in this course, then that's fine. There's a waiver exam. Um, it will be online, it will be through Prairie Learn. If you get a score of zero, you can still say, man, I had a bad day, I still want to wave it. There's no reason to be here if you don't want to be here, if you don't think that I can teach you something. One thing that I will ask is uh, do not share course solutions. Uh, sharing solutions hurts everyone because even though I don't really want to, it will force me to recreate materials and that will reduce the time I have to improve the course in other ways or to create new novel education experiences or to figure out how to better use AI to teach you discrete math. So uh please don't share the course solutions. Um, I mean everything is on on GPT. - Instructor (8/26/25 6:31 PM): So, that's probably good enough for most people. ### Practical Course Logistics and Recitation Activities - Instructor (8/26/25 6:31 PM): So, having said this, uh for now, um Canvas is going to be published soon, I think tonight. Uh you'll be able to join Ed discussion. Um, in uh the recitation, I think, uh we'll set up Overleaf account and do a demo of Latech. You can register your Overleaf account using your Upen address for a free account. Uh, and then please make sure to attend Friday's recitation. So, again, the most important thing will be speed networking with peers and the Latech tutorial. And then the rest of the time will be doing uh brain uh uh brain twisters. So, uh fun puzzles that use discrete math. And then homework one will be released uh very soon and uh you will have about a week to complete it. - Instructor (8/26/25 6:32 PM): So, I just want to um the we haven't yet decided if I will be attending the Friday sessions. I uh need to double check with the TAs. But I wanted to give you a heads up on on what will actually happen. So, in the speed networking uh activity, um we will have you um meet for I think three minutes with seven uh of your peers. So, we'll just have you talk and introduce. We have uh a custom script that you can use or you can have any conversation if you feel comfortable. - Instructor (8/26/25 6:32 PM): But um the idea is for you to have structured time to meet uh new people in the MCIT. Uh, so the goal of that is don't just talk about, you know, um aimless stuff. Go into that speed networking with the intention of uh looking for study partners, looking for people with whom to submit the homeworks. Um, with people with maybe to uh work on the hackathon that will happen uh later this month. Um, so try to start using this to build your support network. The second thing is for the Latech introduction, uh make sure that by the time that that recitation is done that you have an Overleaf account and that you're able to compile some uh basic Latech. ### General Course Support and Feedback - Instructor (8/26/25 6:33 PM): Okay, so now, um thank you. So remember that we're here for your success. Office hours start next week. Use Ed discussion and please uh feedback is always welcome. And so there's um there was this engagement thing. I ask for feedback at the end of every class. Um, I will evaluate it based on how interesting it is, you know? So if you have nothing to say, don't say anything. Uh, don't just say things to fill it out, but if on one week or in one day you're like, hey, I didn't really understand that or I thought you were off your game today, you know? That's useful feedback. And if you tell me why, that's even more useful feedback. ### Addressing Student Questions (Q&A) - Instructor (8/26/25 6:34 PM): Okay. So, now I'm going to look at questions and so we have five questions, which is great. And if any of you want to come up with others, and I'm also going to um start the yeah. - Instructor (8/26/25 6:35 PM): in five minutes, I'll open the survey. So that gives you time, but first let's answer questions. Uh, okay. So if study groups are encouraged, what is the line of homework integrity? Is checking answer allowed? So again, I'm not I I'm not going to uh I'm not going to uh police you. Um, I don't have the time and I don't think you have the interest. It's not in your interest to do that. So, what I'm suggesting that you do is that you become your own police, that you understand when that line is being crossed and like the point of the homework is for you to understand and practice and master a concept. If you're prac if you're engaging in this exercise in a way that leaves you not feeling that way, then you're crossing the line. It it's not really for me to say because we all have different learning styles. Uh, we all have different ways of of acquiring knowledge and so I'm not going to impose anything on you. It it's for you to to um figure it out. Which hackathon is coming? So, um, maybe I'm wrong, but in the three years I've been here, every at the end of every September, the MCIT uh class, uh the senior class organizes a a hackathon. So, it happened the first year I was here, it happened last year. I'm assuming it will happen this year, but maybe, you know, um they'll decide it's too much work and they'll skip a generation. Uh, I would ask uh the so there's an MCIT slack. I would ask uh in a channel in there to see if anybody's planning one. - Instructor (8/26/25 6:36 PM): Would you recommend any AI specifically? Um, I I love Chat GPT and I love Claude and asking me to choose, I would not be able to. Here's what I would say to people. The all of these articles that are telling you, oh, this is the best model or that is the best model is fundamentally stupid. I there is no best, you know? There's a wide variety of very diverse and different models each have different skills. I really like to say that each model has a different personality. You don't realize that there's so many parameters involved in in designing these models. There's all of the data sets, there's the way that they're trained, the the way that they're post-trained, there's the reinforcement learning uh layer on top of it. Then there's the system prompt and then there's the interface. So, asking which is the best model is for somebody that I don't know wants like a summary of like of revolution and I can't do that. So what I do and what I do do a lot of the time is that I will work with one model and then I will copy paste the conversation. I'll give it to another model and I'll say, hey, other model, did we smoke crack? And the other model will will will red team our conversation and we'll say, well, actually, you know, this this doesn't stand or this is actually a very serious conversation. So, I I feel like um I I recommend that you have multiple one. That doesn't mean you have to have multiple paid ones, but if you have the budget, I would say Claude and and and Open AI. - Instructor (8/26/25 6:38 PM): Um, that's no problem. Thank you for the question. So, the slides will be posted but after uh and on the website and the website will be released on Friday or at the end of the week, Sunday. Is this class more focused on math theory or how to apply it on CS? Do you recommend people with math undergrad degree take it or really take real analysis? No. So, thank you for the question. I recommend that you look out for the website and that you take the waiver exam and I think you'll be very confident that you don't need to take this class. So the focus is more on on math theory. So we're we're covering all of the elements of this math discrete math theory so that then in other courses they get the privilege of applying it to uh CS. But nobody else wants to teach this because um it's very complicated to teach the applications at the same time as the principles. - Instructor (8/26/25 6:39 PM): How do we find the course on Ed discussion? Uh that will be on Canvas um once the Canvas is published, but you don't currently have access to it. - Instructor (8/26/25 6:39 PM): Where can we find out about the office hours for you and Mathias? So they will be posted next week uh on the website, but there are no office hours this week. ### Discussion on Machine Learning and Related Courses - Instructor (8/26/25 6:39 PM): Yep. - Instructor (8/26/25 6:39 PM): machine learning relies heavily on linear algebra, but it's not a practice for this course. - Instructor (8/26/25 6:39 PM): Uh yes, I think there's um I forget what the the course uh the the the code of the courses. I'll look it up. - Instructor (8/26/25 6:40 PM): There's a a course called the mathematical foundations of machine learning or something like that, I think. - Instructor (8/26/25 6:40 PM): Yeah, I said undergraduate course. - Instructor (8/26/25 6:40 PM): It's an undergraduate course, yeah. - Instructor (8/26/25 6:40 PM): And you can't take it? - Instructor (8/26/25 6:40 PM): Uh not as part of the degree. - Instructor (8/26/25 6:40 PM): Got it. - Instructor (8/26/25 6:40 PM): Got it. - Instructor (8/26/25 6:40 PM): 5150 might help with that. - Instructor (8/26/25 6:40 PM): 5150. - Instructor (8/26/25 6:40 PM): Thank you. ### Clarifying Friday Class Schedule and Location - Instructor (8/26/25 6:40 PM): Any other questions? - Instructor (8/26/25 6:40 PM): Yep. - Instructor (8/26/25 6:40 PM): So this the Friday special also this time. - Instructor (8/26/25 6:40 PM): No, so um the Friday is uh 10:15 to 11:55 or 45 or something like that. It's in the morning and it's in Moore, so it's uh over the corner. Moore 260. - Instructor (8/26/25 6:40 PM): Uh uh that will be um I'll send an announcement to make sure you all have access to that. - Instructor (8/26/25 6:41 PM): Thank you for the question. - Instructor (8/26/25 6:41 PM): Let me make a note to make an announcement. ### Survey Introduction and Class Dismissal - Instructor (8/26/25 6:41 PM): Are there any other questions? - Instructor (8/26/25 6:41 PM): Okay, well, um feel free to ask a question, but now I will open the the survey. So the the survey will always be the same questions. - Instructor (8/26/25 6:41 PM): The first question is a rating from one to five. What did you think of today's class? - Instructor (8/26/25 6:41 PM): The second question is an open question, which is what did you find most interesting? - Instructor (8/26/25 6:41 PM): And then the last is a piece of feedback, a piece a comment that could be positive or negative or both or neither. - Instructor (8/26/25 6:44 PM): Thank you so much for uh all your feedback. I already see um 58 votes. Um and uh we're now done with class. So um as soon as you're done completing, feel free to leave. Thank you so much and I look forward to seeing you on Thursday.