Join Peggy Fisher for an in-depth discussion in this video Solution: Advanced techniques, part of Programming Foundations: Discrete Mathematics.
- [Voiceover] How did you make out…with the last challenge in the series?…In this challenge,…you had to use a tree…with variable length in coding,…to translate words into binary,…and then take a binary encoded message…and translate it back into plain text.…There was also a challenge…to calculate the probability of events,…using set notation.…And, finally, to encrypt and decrypt…using a Caesar cipher.…Alright, let's take a look at my answers.…Here is the binary tree on the right.…The question was, how do you decode…this binary list of numbers?…Remember, it's a pre-fixed notation.…
So you start, 0-0-1.…So, if I come down,…0-0-1.…0-0-1-1, I get to an S.…When you get to a letter,…you want to stop and start over at the top.…This time, I have four 1s.…Then, I have two more 1s.…So that's going to take me…all the way down to the M.…Then I have three 0s,…which takes me to the A.…Next, I have 1-1-1, 1-1,…but this time, 0.…
That takes me down to the R.…Then I have 1-1-1, 0-0, and a 1,…which is T.…It looks like we spelled the word smart.…
This course relies on an open-source SML (standard machine language) library to demo the concepts behind discrete math. Peggy Fisher shows you how to manipulate sets of data, write proofs and truth tables, analyze data sequences, and visualize data using graph theory. Challenges at the end of every chapter allow you to test your knowledge. By the end of the course, you should be able to make the leap from theory to using discrete math in practice: saving time and resulting in code that's cleaner and easier to maintain in the long run.
- Real-world discrete math
- Objects as sets
- Set notation and operations
- Standard machine language (SML) setup
- Working with data types, strings, and functions in SML
- Analyzing data sequences
- Writing truth tables
- Identifying and evaluating predicates
- Validating arguments
- Writing proofs: subset, conditional, and biconditional proofs
- Visualizing data with graphs
- Advanced discrete math techniques
Skill Level Intermediate
1. Discrete Math Uses
3. Setting Up SML
4. Analyzing Data Sequences
5. Effective Arguments and Defensible Decisions
6. Proofs Made Easy
7. Advanced Discrete Math Topics
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