MATH 1302 — Discrete Mathematics
👋 Welcome to MATH 1302
Hi! If you are going to take MATH 1302 “Discrete Math” at University of the People, then this article is for you. I took this course from April to June of 2020 (during the start of the COVID-19 pandemic) and even though the situation around the world was very unstable, UoPeople classes were not interrupted during this period. Their dedication motivated me and gave the strength I needed to continue my studies during this term, even under these circumstances of uncertainty.
I wanted to take a discrete math course ever since I decided to enroll in this degree. I was particularly interested in learning two topics: logic and graph theory because I found them extremely interesting and applicable to real-world scenarios. This course gave me the opportunity to learn them through an engaging and challenging experience.
Be prepared to work hard during this course. It took me about 20+ hours per week to complete my study sessions and assignments. Like in any math or computer science course, your success depends on your dedication and motivation. Start the course motivated and with the right mindset and you will succeed.👍
A key factor that made this a memorable learning experience was my professor. I was very lucky to have this professor for this particular course. She was extremely engaged, published announcements every week, participated on the discussion forums, and shared links to interesting resources to help us complement our learning. I’m very thankful to her because she motivated me and helped me to stay focused during this difficult time.
📚 Course Content
Let me start by giving you a brief overview of the topics covered during the course. Even if you studied some them in other courses like College Algebra, discrete math will have a new approach using discrete sets and structures, so they are not exactly the same.
In particular, these are the topics covered per week (one unit per week):
- Unit 1: Math Notation and Set Theory
During this week, you will learn basic math notation and how to work with logical connectives, propositional variables, predicates and quantifiers, and what it means for a condition to be necessary and/or sufficient. You will also learn about sets, set notation, and Venn diagrams.
💡 Tip: For Unit 1, I suggest researching online about “necessary vs. sufficient”. This YouTube video was very helpful. I would also suggest researching online about nested quantifiers because they are commonly used in logic.
- Unit 2: Combinatorics
During this week, you will learn how to count. Yes, really. Counting in more complex, real-world applications is completely different from counting like we do every day (1, 2, 3, …). This topic is very interesting. You will learn the additive principle, the multiplicative principle, how to count with sets, the principle of inclusion/exclusion, and how to find binomial coefficients and its applications. You will also learn the difference between permutations and combinations and how to find them in a given problem.
💡 Tips: During this unit, I particularly loved the application of binomial coefficients to lattice paths 💖.
- Unit 3: Logic ⭐
This was one of my favorite weeks of the course. I had almost no previous knowledge of logic and I finished the week being much more confident with my skills. You will learn about truth tables, logical statements, and De Morgan’s Laws.
💡 Tips: My suggestion for this unit is to find and solve as many exercises as possible. Learn how to read and translate written statements into formal mathematical and logical notation using quantifiers. Test yourself constantly because this is one of the most challenging parts of the course .The basic concepts that you learned in Unit 1 will be very helpful during this unit.
- Unit 4: Sequences and Series
During this unit, you will learn how to work with sequences and series. Particularly, arithmetic and geometric sequences. You will learn how to prove a mathematical statement using induction and strong induction.
💡 Tips: It is extremely important that you understand the content of this unit before you start diving into the next unit on recursion because they are closely related. Proving something might seem daunting at first, but with practice you will see that induction is not so complex and that it is an incredibly powerful tool.
- Unit 5: Recursion
If you enrolled in a Computer Science degree, then you have probably heard about or used recursion in code. This week covered recursion from a theoretical point of view, which was awesome. I had never analyzed recurrence relations in detail or found a closed formula for a recurrence relation. Particularly, you will learn how to solve recurrence relations using the iteration method and the characteristic root method. - Unit 6: Functions
During this week, you will review some concepts that you learned in College Algebra such as image, domain, codomain, range, and the classification of functions: injective, surjective, and bijective. You will learn new function notation and the topic will be explained from the perspective of discrete math, so you will be working with discrete sets that have discrete (separate) elements. - Unit 7: Graphs and Graph Theory ⭐
This was definitely my favorite week of the course 💖. If you like computer science, then I think that you will find this week completely fascinating. Graph theory has incredibly diverse real-world applications and during this week you will start diving into this amazing world. You will learn the problem that gave rise to graph theory: The Seven Bridges of Königsberg. You will learn what a subgraph is, the different types of graphs, the handshake lemma, how to color graphs with the minimum number of colors, and how to distinguish Euler paths, Euler circuits, Hamilton Paths, and Hamilton cycles.
💡 Tips: Be prepared to dedicate more study time for this unit because this topic requires more practice and research.
- Unit 8: Number Theory
During this unit, you will learn the mathematical foundation of the RSA Algorithm, the algorithm that is currently used for encryption and decryption. It’s very interesting. You will learn about the division algorithm, divisibility, and congruences. You will practice solving congruences and Diophantine equations.
💡 Tips: Take the necessary time to learn and understand how this encryption algorithm works behind the scenes because its practical applications are amazing. Think about it, you will be learning something that makes our current world possible. Without encryption, you wouldn’t be able to send data securely through a web browser.
- Unit 9: Review and Final Exam
This week you need review all the content of the course and take the final exam. Good luck! ✨
✍️ Study Tips and Helpful Resources
- Take detailed notes of the readings. Develop a note-taking system that will help you review before the quizzes and final exam. Extract the most important information and add your own comments.
- Solve the exercises of each chapter of the textbook. Seriously, they will be very helpful.
- Understanding the topic of each week is crucial for understanding the topic of the coming week, so if you feel like you need to review before moving on, do it before the next week starts.
- The new edition of the textbook includes a new section on trees for Unit 7. I suggest reading it because this knowledge will be very helpful for you when you start taking Programming 2 and Data Structures.
- Learn about Weighted Graphs, Kruskal’s Algorithm, Prim’s Algorithm, and Dijkstra’s Algorithm. Try to implement these algorithms in a programming language of your choice.
These resources were very helpful:
- MIT OCW’s course “Mathematics for Computer Science”. You will find some of the topics explained in this course by MIT. The video lectures and resources are incredibly helpful.
- This YouTube playlist on Graph Theory was very helpful for Unit 7:
I’m currently taking Programming 2, so stay tuned for my next article in just a few weeks.
✨ Good Luck!
I really hope you liked my article. Follow my Medium Publication My UoPeople CS Journey to read about my experience during the degree 🎓.
I wish you much success during this course and during your UoPeople journey! Your claps 👏 are greatly appreciated.
