Midterm exam2 for Discrete Math

 

Topics for Midterm Exam 2

Midterm Exam 2 covers the material that we learned from Chapters 4, 6, and 7 of the textbook. This includes Sections 4.1-4.6, 6.1-6.2, 6.7-6.9, and 7.1-7.3.

Topics from Chapter 4:

  • Functions: domain, target, range
  • Arrow diagrams
  • Floor and ceiling functions
  • Injective, surjective, and bijective functions
  • Inverses of functions
  • Composition of functions
  • Logarithms and exponents (but mainly logarithms)

Topics from Chapter 6:

  • Binary relations on a set
  • Examples of binary relations on graphs and trees
  • Representing binary relations with arrow diagrams and matrices
  • Properties of binary relations: reflexive, anti-reflexive, neither; symmetric, anti-symmetric, neither; transitive or not
  • Order relations: partial vs. total, strict vs. non-strict
  • Equivalence relations and equivalence classes
  • Proving that a relation is (or is not) an order relation or an equivalence relation

Topics from Chapter 7:

  • Asymptotic growth: f is O(g), f is Ω(g), f is Θ(g)
  • Given a complicated function f, finding a simple function g for which f is Θ(g)
  • Proving that f is or is not O(g)
  • Proving that f is or is not Ω(g)
  • Growth hierarchy of functions (e.g. 1.3n = Ω(n5))
  • Computing asymptotic time complexity of algorithms, including algorithms with nested loops

Comments

Post a Comment

Popular posts from this blog

CICD Pipeline - Midterm Exam of Spring 2025 DevOps Class

Image
  Introduction  This project was making CICD pipeline with Git Action, Docker, EC2, RDS, ECR, and Route53. I used my side project Jake (Social Media platform for international students) as source code. The flow of CI/CD pipeline goes like below. Source Repo contains Dockerfile and Docker-Compose.yml. It needs to run locally without any error. Infra Repo contains GitAction workflow codes. This triggers launching a temporary EC2 and fetch codes from source repo. It builds docker files and conducts smoke test. If smoke test succeeds, it pushes docker image to ECR, and it is deployed in EC2 as a QA Server. Route 53 directs IP address to domain name. The Issue  There were many issues and errors while building the CI/CD pipeline.  Source Repo Local test CORS Error : Connecting FrontEnd and BackEnd caused CORS error, which is not letting other origin use same address. To fix it, I used Reverse Proxy by Nginx, and added annotation in SpringBoot controller(@CrossOrigin)....
Read more

Open Source Project - Open Energy Dashboard

Image
  Open Source Project - Open Energy Dashboard Introduction  During last 4 weeks our CTI team (Hyunoh, Abas, Ezequiel, and Mon) worked on Open Energy Dashboard open-source project. Open Energy Dashboard(OED) is a project where it is used as an energy dashboard so that all the users can manage the energy usage of their worksite. ( link ) The Issue  We as a team coded a line group reading test case(c11) in JavaScript and TypeScript using Docker and Visual Studio Code, ensuring values are read correctly to reflect 14 days giving hourly point and middle readings. ( Link )   Test cases are important to enhance accuracy of a software. By writing and updating test case, we estimate we improved test coverage by 30% and enhanced data accuracy by 25% in a Dockerized environment, ensuring seamless integration and reliable energy value processing.  To resolve the issue, our team 1. looked up for development document,  2.starting Docker and activate web and database...
Read more

2025 Spring CS686 DevOps - Final Project

 Final Project Overview -make MSA service -use EKS -Automate -deploy blue-green strategy  -deployment flow : Nightly Build -> QA -> UAT -> Prod  Steps 1. Make MSA codes  Dismantled existing code into three services - backend1, backend2, and frontend 2. By Git Action test and deploy Made GitAction Workflow('Nightly-Build') to start temporary EC2 and test(smoke-test) the code. Used dockers to run three different services and tested if it works. 3. Deploy to QA Server Using GitAction, deployed it on QA server(single EC2 server). Now we can see it at IP address of EC2 instance.  4. Make EKS Cluster and Deploy Blue Service of UAT  Make VPC and EKS Cluster.  Make Node Group. Need to use good enough instance.  Using Git Action and yaml file from Infra repo, apply configuration to running pods on EKS.  Now your microservice is deployed on EKS and you can access it through url.  5. Switch it to Green Service of UAT  Deployment of Gr...
Read more