This Statistics resource was developed under the guidance and support of experienced high school teachers and subject matter experts. It is presented here in multiple formats: PDF, online, and low-cost print. Statistics offers instruction in grade-level appropriate concepts and skills in a logical, engaging progression that begins with sampling and data and covers topics such as probability, random variables, the normal distribution, and hypothesis testing. This content was developed with students in mind, incorporating statistics labs, worked exercises, and additional opportunities for assessment that incorporate real-world statistical applications. For instructors, resources are available to support the implementation of the Statistics textbook, including a Getting Started Guide, direct instruction presentations, and a solutions manual.

The typical introductory real analysis text starts with an analysis of the real number system and uses this to develop the definition of a limit, which is then used as a foundation for the definitions encountered thereafter. While this is certainly a reasonable approach from a logical point of view, it is not how the subject evolved, nor is it necessarily the best way to introduce students to the rigorous but highly non-intuitive definitions and proofs found in analysis.

This book proposes that an effective way to motivate these definitions is to tell one of the stories (there are many) of the historical development of the subject, from its intuitive beginnings to modern rigor. The definitions and techniques are motivated by the actual difficulties encountered by the intuitive approach and are presented in their historical context. However, this is not a history of analysis book. It is an introductory analysis textbook, presented through the lens of history. As such, it does not simply insert historical snippets to supplement the material. The history is an integral part of the topic, and students are asked to solve problems that occur as they arise in their historical context.

This book covers the major topics typically addressed in an introductory undergraduate course in real analysis in their historical order. Written with the student in mind, the book provides guidance for transforming an intuitive understanding into rigorous mathematical arguments. For example, in addition to more traditional problems, major theorems are often stated and a proof is outlined. The student is then asked to fill in the missing details as a homework problem.

This exercise book contains a wide variety of problems in integral calculus, linear algebra, and linear regression, with applications to differential equations, probability, and life sciences. Every problem has a very detailed solution, and the book is self-contained, as the summary for every concept is provided. The book aims to help students learn the material more efficiently and get better results.

An Open Education Resource

Short Description:
Mathematical modelling plays an increasingly important role in almost any area of life sciences, and this interactive textbook focuses on the areas of population ecology, infectious diseases, immunology and cell dynamics, gene networks and pharmacokinetics. It is aimed at anyone who is interested in learning about how to model biological systems, including undergraduate and postgraduate mathematics students who have not studied mathematical biology before, life-sciences students with an interest in modelling, and post-16 mathematics students interested in university-level material. Some mathematical knowledge is assumed, and the mathematical models used are all in the form of ordinary differential equations.

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Word Count: 72364

(Note: This resource's metadata has been created automatically by reformatting and/or combining the information that the author initially provided as part of a bulk import process.)

This is an open-source graduate level textbook covering the fundamentals of incompressible fluid flow. The topics cover the derivation of conservation mass, momentum, and energy equations, kinematics of fluid motion, non-dimensionalization and order-of-magnitude analysis, Stokes flows, potential flows, and boundary layers. The textbook was developed for a graduate level course at the Colorado School of Mines Department of Mechanical Engineering. We try to build from the typical math proficiency of incoming grad students, many of whom have never taken a course in PDEs, and may not be comfortable with vector operations such as the gradient, divergence, and Laplacian. Please feel free to contact Nils Tilton at ntilton@mines for any suggested revisions. We can share the latex files as well if you wish to modify the textbook for your own purposes.

Our goal with this textbook is to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs.
The textbook contain topics of real analysis usually covered in a 10-week course: the completeness axiom, sequences and convergence, continuity, and differentiation. The lecture notes also contain many well-selected exercises of various levels. Although these topics are written in a more abstract way compared with those available in some textbooks, teachers can choose to simplify them depending on the background of the students. For instance, rather than introducing the topology of the real line to students, related topological concepts can be replaced by more familiar concepts such as open and closed intervals. Some other topics such as lower and upper semicontinuity, differentiation of convex functions, and generalized differentiation of non-differentiable convex functions can be used as optional mathematical projects. In this way, the lecture notes are suitable for teaching students of different backgrounds.

Psychology students often find statistics courses to be different from their other psychology classes. There are some distinct differences, especially involving study strategies for class success. The first difference is learning a new vocabulary—it is similar to learning a new language. Knowing the meaning of certain words will help as you are reading the material and working through the problems. Secondly, practice is critical for success; reading over the material is not enough. Statistics is a subject learned by doing, so make sure you work through any homework questions, chapter questions, and practice problems available. Lastly, we recommend that you ask questions and get help from your instructor when needed. Struggling with the course material can be frustrating, and frustration is your enemy. Often your instructor can get you back on track quickly.

Introductory Business Statistics is designed to meet the scope and sequence requirements of the one-semester statistics course for business, economics, and related majors. Core statistical concepts and skills have been augmented with practical business examples, scenarios, and exercises. The result is a meaningful understanding of the discipline, which will serve students in their business careers and real-world experiences.

The book "Introductory Business Statistics" by Thomas K. Tiemann explores the basic ideas behind statistics, such as populations, samples, the difference between data and information, and most importantly sampling distributions. The author covers topics including descriptive statistics and frequency distributions, normal and t-distributions, hypothesis testing, t-tests, f-tests, analysis of variance, non-parametric tests, and regression basics. Using real-world examples throughout the text, the author hopes to help students understand how statistics works, not just how to "get the right number."

"Introductory Business Statistics with Interactive Spreadsheets - 1st Canadian Edition" is an adaptation of Thomas K. Tiemann's book, "Introductory Business Statistics". In addition to covering basics such as populations, samples, the difference between data and information, and sampling distributions, descriptive statistics and frequency distributions, normal and t-distributions, hypothesis testing, t-tests, f-tests, analysis of variance, non-parametric tests, and regression basics, the following information has been added: the chi-square test and categorical variables, null and alternative hypotheses for the test of independence, simple linear regression model, least squares method, coefficient of determination, confidence interval for the average of the dependent variable, and prediction interval for a specific value of the dependent variable. This new edition also allows readers to learn the basic and most commonly applied statistical techniques in business in an interactive way -- when using the web version -- through interactive Excel spreadsheets. All information has been revised to reflect Canadian content.

Introductory Statistics follows scope and sequence requirements of a one-semester introduction to statistics course and is geared toward students majoring in fields other than math or engineering. The text assumes some knowledge of intermediate algebra and focuses on statistics application over theory. Introductory Statistics includes innovative practical applications that make the text relevant and accessible, as well as collaborative exercises, technology integration problems, and statistics labs.

Adapted from the OpenStax Textbook for the College of Lake County's Introductory Statistics course (Susan Dean and Barbara Illowsky (Published 2013 by OpenStax College)).

"An Intuitive, Interactive Introduction to Biostatistics" is an introductory statistics textbook oriented towards towards undergraduate students in the health sciences. While covering the breadth of material typically presented in a first semester statistics course, including introductions to probability and distributions, study design, CLT, hypothesis testing, and inference, IIIB distinguishes itself with its focus on cultivating student intuition through the use of guided questions and interactive simulation-based applets. Written in R, this open-source text has been created with customizability in mind, offering instructors maximal flexibility in arranging and modifying the content.

These are lecture notes for cs427 at Oregon State University, an introductory course in cryptography at the advanced undergraduate level. By reading and studying these notes, you should expect to learn how to:

*State and interpret the standard formal definitions for the most common cryptographic security properties (privacy and authentication).
*Formally prove security properties of sound cryptographic constructions, and break the security of unsound ones.
*Choose the appropriate cryptographic primitive for a task (block ciphers, hash functions, MACs, public-key encryption, etc.) while avoiding common pitfalls.
*Along the way, you will also learn how the most common cryptographic constructions work.

Learning Statistics with JASP is a free textbook covering the basics of statistical inference for beginners in psychology and related applied disciplines. It uses the free software package JASP. Written in a lively, conversational style, it provides the reader with a perfect balance of readability and rigor, and gives students a modern view of statistical inference in the psychological and behavioral sciences.

This textbook covers the contents of an introductory statistics class, as typically taught to undergraduate psychology, health or social science students. The book covers how to get started in jamovi as well as giving an introduction to data manipulation. From a statistical perspective, the book discusses descriptive statistics and graphing first, followed by chapters on probability theory, sampling and estimation, and null hypothesis testing. After introducing the theory, the book covers the analysis of contingency tables, correlation, t-tests, regression, ANOVA and factor analysis. Bayesian statistics are touched on at the end of the book.

Vakinhoud:
- Leren rekenen met vectoren en matrices.
- De methode van rijreductie voor het oplossen van lineaire systemen.
- De begrippen lineair onafhankelijk, span en basis
- Elementaire lineaire transformaties, de begrippen surjectief en injectief.
- De begrippen deelruimte, basis en dimensie en voorbeelden hiervan.
- Eigenwaardes en eigenvectoren van een matrix.
- Dit vak is een combinatie van de vakken Lineaire Algebra 1 en Lineaire Algebra 2 die bij andere TU-opleidingen aangeboden worden.

Leerdoelen:
- Het kennen van basisbegrippen, het gebruik van basismethodes.
- Het maken van logische afleidingen met behulp van deze begrippen en methodes

Welcome to this online course on Linear Algebra.

Linear Algebra is a branch of mathematics that plays a fundamental to role in many parts of Science and Engineering, such as Quantum Mechanics, Coding Theory, Signal Processing and Control Theory .

As Linear Algebra is a common component of many university programmes in Science or Engineering, this course can be used as additional study or preparation for on campus courses on Linear Algebra. Please note that we cannot guarantee that this course can replace an on campus course.

The course has no preliminaries other than basic high school mathematics. Furthermore, the course is self contained; it can be studied without extra resources. Nevertheless, for each topic you can find some references to standard literature that you can consult for further reading.

This is a web-based, interactive, introductory linear algebra text. Interactive elements include auto-graded exercises, built-in GeoGebra activities, and Octave code. Topics include vectors and matrices, linear systems, vector spaces (R^n and abstract), linear transformations, eigenvalues, orthogonality, and determinants. Strong emphasis is placed on geometry and visualization. Several applications are included, and links to numerous applications are provided. To access the text, please visit https://sites.google.com/view/lin-alg-interactive-intro/