Iteration 

Register Machines

Closure

Zero Space

Minimization

First-order logic

Logic

Infinite Words

Groups

Polya Counting

Feedback Shift Registers

Coding Theory

Effective Resistance

Hypercomputation

Decidability

Nondeterminism

Computation & Discrete Math

Primitive Recursion

Orbits

Automata

Determinization

Finite Fields

15-354 Computation & Discrete Math Carnegie Mellon University Spring 2021 This advanced course reexamines traditional concepts of discrete mathematics (relations, functions, logic, graphs, algebra, automata) in the context of computation and algorithms, necessitating a strong background in discrete math. In a nutshell, the main idea behind this course is that the development of the digital computer, together with the theory of computation, is also one of the most important developments in mathematics in the 20th century. Consequently, this course takes a fresh look at some of the standard concepts of discrete mathematics (relations, functions, logic, graphs, algebra, automata), with strong and consistent emphasis on computation and algorithms. Another key concern is knowledge transfer: we need to realign traditional mathematical concepts with our new computational universe and find ways to apply ideas from one realm to the other. We begin with a brief introduction to computability and computational complexity. Other topics may include: iteration, orbits and fixed points; order and equivalence relations; transition systems; groups and actions; finite fields, randomness; propositional logic and satisfiability testing.

To get a better impression, take a look at some of the homework problems that were used in previous versions of this course: [CDM Assignments](https://www.cs.cmu.edu/~sutner/CDM/notes/hw-master-nosol.pdf). A few pictures can be found here: [CDM Gallery](https://www.cs.cmu.edu/~sutner/CDM/bilder.html) (challenge: figure out what these pictures mean, for as many as you can manage). A slightly dated paper outlining the course philosophy can be found at [Jeric](http://www.cs.cmu.edu/~sutner/papers/JERIC05.pdf).

Needless to say, a solid background in discrete math is necessary for this course. You should feel very much at home with all the 15-251 material.   

15-354 Computation & Discrete Math

Mathematical Foundations

Histograms

Pivots

Models

P-Value

Confidence Intervals

Sample Means

Least Squares

Privacy

Bayes' theorem

Data type

Census

Function (computer programming)

Joins

Chance

Comparing Distributions

A/B Testing

Center and Spread

Correlation

Residuals

Classification

Conditional probability

Tables

Charts

Conditional (computer programming)

Sampling

Decisions

Causality

Normal distribution

Linear regression

Regression Inference

Classifiers

Data 8: The Foundations of Data Science UC Berkeley Fall 2022 UC Berkeley's course blends inferential thinking, computational thinking, and real-world relevance, offering students hands-on analysis of real-world datasets. It covers critical concepts in computer programming, statistical inference, privacy, and study design. Foundations of Data Science combines three perspectives: inferential thinking, computational thinking, and real-world relevance. Given data arising from some real-world phenomenon, how does one analyze that data so as to understand that phenomenon? The course teaches critical concepts and skills in computer programming and statistical inference, in conjunction with hands-on analysis of real-world datasets, including economic data, document collections, geographical data, and social networks. It also delves into social issues surrounding data analysis such as privacy and study design.  This course does not have any prerequisites beyond high-school algebra. The curriculum and format is designed specifically for students who have not previously taken statistics or computer science courses. Students with some prior experience in either statistics or computing are welcome to enroll and will find much of interest due to the innovative nature of the course. Students who have taken several statistics or computer science courses should instead take a more advanced course. Our primary text is an online book called [Computational and Inferential Thinking: The Foundations of Data Science](http://inferentialthinking.com/). This text was written for the course by the course instructors. A complete PDF of the textbook can be found in the Student Materials Google Drive.

The computing platform for the course is hosted at [data8.datahub.berkeley.edu](file:///Users/jweichert/Desktop/Data%208/data-8.github.io/fa22/data8.datahub.berkeley.edu). Students find it convenient to use their own computer for the course. If you do not have adequate access to a personal computer, we can help you borrow a machine; please contact data8@berkeley.edu.

Data 8: The Foundations of Data Science

Data Science

Iteration

Iteration

2 courses cover this concept

15-354 Computation & Discrete Math

Data 8: The Foundations of Data Science