IntroductionSP22 MATH/CS 240: Discrete MathematicsUW-MadisonSP22 MATH/CS 240: Discrete Mathematics Introduction 1 / 13About meFirst name: Jun Le. Last name: Goh.吴均乐He/himSingaporeMasters in computer sciencePhD in mathematicsOffice hours on Thu 4-5 PM and Fri 2:30-3:30 PM in Van Vleck B223SP22 MATH/CS 240: Discrete Mathematics Introduction 2 / 13Why study mathematics?Reality is very complicated. We want to understand it.There are two closely related aspects of mathematics:1Abstracting features of interest from a complicated reality (“modeling”)2Given a model, determining its properties and behavior (“solving”)Mathematics is a methodology, not just a collection of formulas.SP22 MATH/CS 240: Discrete Mathematics Introduction 3 / 13Why study discrete mathematics?How do we use computers to solve problems?How does Maps figure out the best way for you to get from point A to point B?1Collect data (what type of data?)2Encode the data in some data structure(what determines whether the data structure is suitable?)3Calculate an optimal route(what determines whether a route is optimal?)Discrete mathematics is essential for several steps in the above process.SP22 MATH/CS 240: Discrete Mathematics Introduction 4 / 13Why study discrete mathematics?1It is useful for modeling problems that computers can solve2It is useful for modeling and understanding the behavior of computer programsHow do we know that programs are working as intended?Can we estimate how much resources (time, space) a program will need?3It is useful for approximating the continuousSP22 MATH/CS 240: Discrete Mathematics Introduction 5 / 13Skills that you will acquire in this course1Mathematical reasoningHow to understand and craft mathematical argumentsThis includes short proofs2Combinatorial analysisHow to count3Understanding of discrete structuresSets, functions, sequences, relations, graphs, trees, finite-state machines4Algorithmic thinkingUsing algorithms to solve problemsReasoning about properties of algorithmsSP22 MATH/CS 240: Discrete Mathematics Introduction 6 / 13What knowledge from previous courses will be useful?I will assume you are fluent in college algebra:fractions, inequalities, rational numbers, polynomials, exponentials, logarithms,etc.Experience in proofs will be helpful but I will not assume you have any.The following will neither be taught nor tested:ProgrammingDerivatives and integralsSP22 MATH/CS 240: Discrete Mathematics Introduction 7 / 13Course policiesLecture policies:Raise your hand if you have a question or want to offer an answerDo not hinder others from learningFeedback is encouraged:Let us know how we can help you learn betterHomework policies:Collaboration is encouraged, subject to the rules belowState the names of the students you collaborated withAll solutions for written HW have to be written out individuallyDo not consult outside sources, other than your textbook and lecture slidesSP22 MATH/CS 240: Discrete Mathematics Introduction 8 / 13How to succeedBelieve in your ability to succeed.Go to lectures and discussion section.Read the relevant sections in the textbook before lecture.Seek support!Your classmates (in person, Piazza)Your TAs and myself (office hours, Piazza)Calculus Lab (https://math.wisc.edu/undergraduate/mlc/drop-in/)To prepare for exams, do new exercises (e.g., from the textbook) rather thanjust reading homework solutions.Tips:Only reading the textbook and/or taking notes from lecture does not provideenough understanding to do well in the course.Don’t give up too early. Some amount of frustration is normal. Only seek supportonce you have made some effort to solve a problem.SP22 MATH/CS 240: Discrete Mathematics Introduction 9 / 13Textbook: zyBookWe will use an online textbook called a zyBook.Please follow the instructions in the Overview page on Canvas to buy it. The cost is 58USD.You need to buy the textbook using our code (provided on Canvas) in order tosubmit a significant portion of homework.SP22 MATH/CS 240: Discrete Mathematics Introduction 10 / 13Participation activities and homework10% of your final grade is based on zyBook participation activities due at 1pm(before some lectures).For example, the participation activities for 1.6–1.8 are due next Monday (1/31) at1pm.20% of your final grade is based on homework. Each HW has ≤ 2 components, bothdue approximately every Friday at 2359:1zyBook challenge activities (zyBook)2written homework (Canvas).HW0 is entirely on zyBook. Subsequent HWs will be split between zyBook and Canvas.We will drop the three lowest HW scores when calculating your final grade.SP22 MATH/CS 240: Discrete Mathematics Introduction 11 / 13Changing section, waitlist, etc.Email Kyle Martinez at [email protected] MATH/CS 240: Discrete Mathematics Introduction 12 / 13Todo for you1Read the syllabus and Overview page on Canvas2Buy our zyBook using our code on Canvas (58 USD)3Enroll in our class Piazza4Work on participation activities for 1.6–1.8 and 1.9–1.11, as well as HW0 (all onzyBook)SP22 MATH/CS 240: Discrete Mathematics Introduction 13 /