Join Peggy Fisher for an in-depth discussion in this video Sequences and sums, part of Programming Foundations: Discrete Mathematics.
- [Voiceover] Sequences and sums.…Often, sets contain sequences of numbers.…These sequences can be finite, or infinite.…A finite sequence has an initial index value of m,…and a final index value, n, which must be…greater than or equal to m.…The value of m starts with one and goes to n.…I want to point out that this represents the placeholder…for the number in the sequence, it is not related to…the actual value of the number in the sequence.…
It is often helpful to define a sequence…using an explicit formula showing how term a-sub-k…depends on the position in the sequence…denoted by the value, k.…Given this sequence, two to the first, two-squared,…two-cubed, we want to consider an explicit forumla…for this series.…If you look at the first element in the list,…it's two raised to the first power.…The second element is two raised to the second power,…et cetera.…
We can represent each element in this series…as d-sub-k, meaning the element in the list…in the k's position is equal to…two raised to the k value for all k…
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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