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2017
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Video
Irina Kareva translates biology into mathematics and vice versa. She writes mathematical models that describe the dynamics of cancer, with the goal of developing new drugs that target tumors. "The power and beauty of mathematical modeling lies in the fact that it makes you formalize, in a very rigorous way, what we think we know," Kareva says. "It can help guide us to where we should keep looking, and where there may be a dead end." It all comes down to asking the right question and translating it to the right equation, and back.
- Subjects:
- Health Sciences and Mathematics and Statistics
- Keywords:
- Cancer -- Mathematical models Cancer cells -- Mathematical models
- Resource Type:
- Video
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e-book
Math in Society is a free, open textbook. This book is a survey of contemporary mathematical topics, most non-algebraic, appropriate for a college-level topics course for liberal arts majors. The text is designed so that most chapters are independent, allowing the instructor to choose a selection of topics to be covered. Emphasis is placed on the applicability of the mathematics. Core material for each topic is covered in the main text, with additional depth available through exploration exercises appropriate for in-class, group, or individual investigation. This book is appropriate for Math 107 (Washington State Community Colleges common course number).
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematics Textbooks
- Resource Type:
- e-book
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Courseware
How do populations grow? How do viruses spread? What is the trajectory of a glider? Many real-life problems can be described and solved by mathematical models. In this course, you will form a team with another student and work in a project to solve a real-life problem. You will learn to analyze your chosen problem, formulate it as a mathematical model (containing ordinary differential equations), solve the equations in the model, and validate your results. You will learn how to implement Euler’s method in a Python program. If needed, you can refine or improve your model, based on your first results. Finally, you will learn how to report your findings in a scientific way. This course is mainly aimed at Bachelor students from Mathematics, Engineering and Science disciplines. However it will suit anyone who would like to learn how mathematical modeling can solve real-world problems.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematical models
- Resource Type:
- Courseware
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e-book
"This is a calculus-based book meant for the first semester of a first year survey course taken by engineering and physical science majors. It has a traditional order of topics whereby force is discussed before energy. It is divided into 17 chapters that cover a review of high school physics, scaling and estimation, vectors, velocity, acceleration, forces, circular motion, gravity, conservation of energy, work, conservation of momentum and angular momentum, vibrations, and resonance. A treatment of relativity is interspersed with the Newtonian mechanics, in optional sections"--BC Campus website.
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e-book
In this textbook the focus will be on the bacteria and archaea (traditionally known as the “prokaryotes,”) and the viruses and other acellular agents.
- Subjects:
- Biology
- Keywords:
- Microbiology Textbooks
- Resource Type:
- e-book
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e-book
Microbiology for Allied Health Students is designed to cover the scope and sequence requirements for the single semester Microbiology course for non-majors and allied health students. The book presents the core concepts of microbiology with a focus on applications for careers in allied health. The pedagogical features of Microbiology for Allied Health Students make the material interesting and accessible to students while maintaining the career-application focus and scientific rigor inherent in the subject matter. The scope and sequence of Microbiology for Allied Health Students has been developed and vetted with input from numerous instructors at institutions across the U.S. It is designed to meet the needs of most microbiology courses allied health students. With these objectives in mind, the content of this textbook has been arranged in a logical progression from fundamental to more advanced concepts. The opening chapters present an overview of the discipline, with individual chapters focusing on cellular biology as well as each of the different types of microorganisms and the various means by which we can control and combat microbial growth. The focus turns to microbial pathogenicity, emphasizing how interactions between microbes and the human immune system contribute to human health and disease. The last several chapters of the text provide a survey of medical microbiology, presenting the characteristics of microbial diseases organized by body system.
- Subjects:
- Biology
- Keywords:
- Allied health personnel Microbiology Textbooks
- Resource Type:
- e-book
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Courseware
This is the first semester of a one year graduate course in number theory covering standard topics in algebraic and analytic number theory. At various points in the course, we will make reference to material from other branches of mathematics, including topology, complex analysis, representation theory, and algebraic geometry.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Number theory Algebraic number theory
- Resource Type:
- Courseware
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Courseware
Are you an engineer, scientist or technician? Are you dealing with measurements or big data, but are you unsure about how to proceed? This is the course that teaches you how to find the best estimates of the unknown parameters from noisy observations. You will also learn how to assess the quality of your results. TU Delft’s approach to observation theory is world leading and based on decades of experience in research and teaching in geodesy and the wider geosciences. The theory, however, can be applied to all the engineering sciences where measurements are used to estimate unknown parameters. The course introduces a standardized approach for parameter estimation, using a functional model (relating the observations to the unknown parameters) and a stochastic model (describing the quality of the observations). Using the concepts of least squares and best linear unbiased estimation (BLUE), parameters are estimated and analyzed in terms of precision and significance. The course ends with the concept of overall model test, to check the validity of the parameter estimation results using hypothesis testing. Emphasis is given to develop a standardized way to deal with estimation problems. Most of the course effort will be on examples and exercises from different engineering disciplines, especially in the domain of Earth Sciences. This course is aimed towards Engineering and Earth Sciences students at Bachelor’s, Master’s and postgraduate level.
- Keywords:
- Observers (Control theory) Mathematical statistics
- Resource Type:
- Courseware
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e-book
"The first edition of this textbook, called Open Genetics, was produced in January 2009 as an instructional material for students in Biology 207 at the University of Alberta. Since then, the book has been built upon and redesigned by numerous adapting authors. Open Genetics Lectures (OGL) is an alternative approach to an open source textbook with much of its content being derived from the original Open Genetics textbook. The 13 chapters in OG were cut up and distributed into 41 shorter chapters that parallel the current lecture topics in BIOL 207 (Molecular Genetics and Heredity) at the University of Alberta. More text content, figures, and chapter-end questions were added in this revision"--BC Campus website.
- Subjects:
- Biology
- Keywords:
- Molecular genetics Textbooks
- Resource Type:
- e-book
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e-book
This book consists of ten weeks of material given as a course on ordinary differential equations (ODEs) for second year mathematics majors at the University of Bristol. It is the first course devoted solely to differential equations that these students will take. This book consists of 10 chapters, and the course is 12 weeks long. Each chapter is covered in a week, and in the remaining two weeks I summarize the entire course, answer lots of questions, and prepare the students for the exam. I do not cover the material in the appendices in the lectures. Some of it is basic material that the students have already seen that I include for completeness and other topics are "tasters" for more advanced material that students will encounter in later courses or in their project work. Students are very curious about the notion of chaos, and I have included some material in an appendix on that concept. The focus in that appendix is only to connect it with ideas that have been developed in this course related to ODEs and to prepare them for more advanced courses in dynamical systems and ergodic theory that are available in their third and fourth years.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Differential equations Textbooks Differential equations Partial
- Resource Type:
- e-book