This book aims to be an accessible introduction into the design and analysis of efficient algorithms. Throughout the book we will introduce only the most basic techniques and describe the rigorous mathematical methods needed to analyze them.

The topics covered include:

The divide and conquer technique.
The use of randomization in algorithms.
The general, but typically inefficient, backtracking technique.
Dynamic programming as an efficient optimization for some backtracking algorithms.
Greedy algorithms as an optimization of other kinds of backtracking algorithms.
Hill-climbing techniques, including network flow.

The goal of the book is to show you how you can methodically apply different techniques to your own algorithms to make them more efficient. While this book mostly highlights general techniques, some well-known algorithms are also looked at in depth. This book is written so it can be read from "cover to cover" in the length of a semester, where sections marked with a * may be skipped.

This textbook is an introductory coverage of algorithms and data structures with application to graphics and geometry.

This web page contains a free electronic version of my self-published textbook Algorithms, along with other lecture notes I have written for various theoretical computer science classes at the University of Illinois, Urbana-Champaign

Animation is a compelling and effective form of expression; it engages viewers and makes difficult concepts easier to grasp. Today’s animation industry creates films, special effects, and games with stunning visual detail and quality. This graduate class will investigate the algorithms that make these animations possible: keyframing, inverse kinematics, physical simulation, optimization, optimal control, motion capture, and data-driven methods. Our study will also reveal the shortcomings of these sophisticated tools. The students will propose improvements and explore new methods for computer animation in semester-long research projects. The course should appeal to both students with general interest in computer graphics and students interested in new applications of machine learning, robotics, biomechanics, physics, applied mathematics and scientific computing.

On its own, a huge DNA sequence is a meaningless pile of data — so, how do biologists figure out what it means? They turn to the power of bioinformatics! In this episode, we’ll learn what bioinformatics is, how it works, and how scientists have used it to better understand everything from evolution to a viral epidemic.
Chapters:
Introduction: Pizza Data
Bioinformatics
Algorithms
The Human Genetic Code
The BRCA1 Gene
Transcriptomes
The Zika Virus
Bioinformatics & Programming
Review & Credits
Credits

This is the third of three lessons that make the connection between programming and algorithms. In this lesson students continue to work with the "Human Machine Language" to get creative designing more algorithms for playing cards. One command is added to the language from the previous lesson (SWAP) that allows positions of cards to change. With the addition of swap the challenge is to design an algorithm that will move the minimum card to the front of the list while keeping the relative order of all the other cards the same. If that is achieved some other Human Machine Language challenges are available.

This resource provides short lessons covering a range of topics from algorithmic thinking to computer processing, with the goal of providing essential computing education without the need for screens. We hope to equip younger children with computational skills, preparing them to tackle modern societal issues and contribute positively to the workforce of tomorrow. By providing an accessible curriculum focusing on topics in computer science, we hope to eliminate barriers preventing students from achieving their full potential in this field.  

This course covers the algorithmic and machine learning foundations of computational biology combining theory with practice. We cover both foundational topics in computational biology, and current research frontiers. We study fundamental techniques, recent advances in the field, and work directly with current large-scale biological datasets.

All of the mathematics required beyond basic calculus is developed “from scratch.” Moreover, the book generally alternates between “theory” and “applications”: one or two chapters on a particular set of purely mathematical concepts are followed by one or two chapters on algorithms and applications; the mathematics provides the theoretical underpinnings for the applications, while the applications both motivate and illustrate the mathematics. Of course, this dichotomy between theory and applications is not perfectly maintained: the chapters that focus mainly on applications include the development of some of the mathematics that is specific to a particular application, and very occasionally, some of the chapters that focus mainly on mathematics include a discussion of related algorithmic ideas as well.

The mathematical material covered includes the basics of number theory (including unique factorization, congruences, the distribution of primes, and quadratic reciprocity) and of abstract algebra (including groups, rings, fields, and vector spaces). It also includes an introduction to discrete probability theory—this material is needed to properly treat the topics of probabilistic algorithms and cryptographic applications. The treatment of all these topics is more or less standard, except that the text only deals with commutative structures (i.e., abelian groups and commutative rings with unity) — this is all that is really needed for the purposes of this text, and the theory of these structures is much simpler and more transparent than that of more general, non-commutative structures.

With the growing availability and lowering costs of genotyping and personal genome sequencing, the focus has shifted from the ability to obtain the sequence to the ability to make sense of the resulting information. This course is aimed at exploring the computational challenges associated with interpreting how sequence differences between individuals lead to phenotypic differences in gene expression, disease predisposition, or response to treatment.

This is a lesson plan designed for 3rd-5th graders that focuses on the core concepts of robots and what it takes to code them. Students build an understanding of algorithms and how to write a sequence of steps in order to accomplish a task. The lesson plan includes four vocabulary words that are regularly used in the lesson, a group Kahoot game to master these words, and instructions and handouts for a "code your friend" game where students get to pretend to be the robot.

The lesson takes 45 minutes.

Vocabulary:
Algorithm: a list of steps to finish a task
Program: an algorithm that has been coded into something that can be run by a machine
Bug: part of a program that does not work correctly
Debugging: finding and fixing problems in an algorithm or program

Resources (also included in the plan)
Nearpod Presentation
https://share.nearpod.com/qlLTPeI79R
Kahoot Vocab
https://play.kahoot.it/#/k/9d5000e6-5412-4776-8bd8-54a5962ccca1
Stacking Cup Ideas Handout
https://docs.google.com/document/d/1nhgt_BfbOmj4lCrcYRC5_QdXsbUbUnNbrMTK9qyFpmE/edit?usp=sharing

Standards:
3-5.DI.2 Develop a simple understanding of an algorithm (e.g., search, sequence of events, or
sorting) using computer-free exercises.

3-5.DI.1 Understand and use the basic steps in algorithmic problem solving (e.g., problem
statement and exploration, examination of sample instances, design, implementation, and
testing).

3-5.CD.2 Understand the pervasiveness of computers and computing in daily life (e.g., voicemail,
downloading videos and audio files, microwave ovens, thermostats, wireless Internet, mobile
computing devices, GPS systems).

Assignments, notes, and exam questions for CS 315: Data Structures and Algorithms. Taught by Raphael Finkel, Department of Computer Science, University of Kentucky.

Students explore the concept of optical character recognition (OCR) in a problem-solving environment. They research OCR and OCR techniques and then apply those methods to the design challenge by developing algorithms capable of correctly "reading" a number on a typical high school sports scoreboard. Students use the structure of the engineering design process to guide them to develop successful algorithms. In the associated activity, student groups implement, test and revise their algorithms. This software design lesson/activity set is designed to be part of a Java programming class.

Testing is critical to any design, whether the creation of new software or a bridge across a wide river. Despite risking the quality of the design, the testing stage is often hurried in order to get products to market. In this lesson, students focus on the testing phase of the software/systems design process. They start by exploring existing examples of program testing using the CodingBat website, which contains a series of problems and challenges that students solve using the Java programming language. Working in teams, students practice writing test cases for other groups' code, and then write test cases for a program before writing the program itself.

The course covers the basic models and solution techniques for problems of sequential decision making under uncertainty (stochastic control). We will consider optimal control of a dynamical system over both a finite and an infinite number of stages. This includes systems with finite or infinite state spaces, as well as perfectly or imperfectly observed systems. We will also discuss approximation methods for problems involving large state spaces. Applications of dynamic programming in a variety of fields will be covered in recitations.

This resource is a video abstract of a research paper created by Research Square on behalf of its authors. It provides a synopsis that's easy to understand, and can be used to introduce the topics it covers to students, researchers, and the general public. The video's transcript is also provided in full, with a portion provided below for preview:

"Our microbiome has profound impacts on our health, and technological advances have allowed for ever-growing pools of data from microbiome-wide studies. This means that our microbiome could be used to estimate disease risk, but the nature of the data makes the endeavor difficult. Similar issues with using genetics to predict disease risk led to the development of the polygenic risk score. Motivated by the success of that framework, a team of researchers recently developed the microbial risk score (MRS). MRS summarizes the complex microbial profile by first identifying a sub- community consisting of disease-associated microbial taxa and then integrating those microbial taxa into a continuous score based on the alpha diversity of the identified sub-community. MRS can be easily integrated with the other risk scores built upon metatranscriptomics, host genetics, or host transcriptomics, making it useful for 'multi-omics' approaches as well..."

The rest of the transcript, along with a link to the research itself, is available on the resource itself.

In this presentation and discussion for high school students, students will learn a simple definition for algorithm and discuss the ways that algorithms shape social media content. Students will question whether the algorithms in their own social media allow them to pursue their interests or limit them. Students will explore ways to adjust settings, privacy and ad preferences to affect the algorithms in the platforms they use. 

This subject describes and illustrates computational approaches to solving problems in systems biology. A series of case-studies will be explored that demonstrate how an effective match between the statement of a biological problem and the selection of an appropriate algorithm or computational technique can lead to fundamental advances. The subject will cover several discrete and numerical algorithms used in simulation, feature extraction, and optimization for molecular, network, and systems models in biology.

This is a foundation subject in modern software development techniques for engineering and information technology. The design and development of component-based software (using C# and .NET) is covered; data structures and algorithms for modeling, analysis, and visualization; basic problem-solving techniques; web services; and the management and maintenance of software. Includes a treatment of topics such as sorting and searching algorithms; and numerical simulation techniques. Foundation for in-depth exploration of image processing, computational geometry, finite element methods, network methods and e-business applications. This course is a core requirement for the Information Technology M. Eng. program.
This class was also offered in Course 13 (Department of Ocean Engineering) as 13.470J. In 2005, ocean engineering subjects became part of Course 2 (Department of Mechanical Engineering), and the 13.470J designation was dropped in lieu of 2.159J.