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### MA212: Linear Algebra II

Saylor.org Free Closed [?] Mathematics

Linear algebra is the study of vector spaces and linear mappings between them.  In this course, we will begin by reviewing topics you learned in Linear Algebra I, starting with linear equations, followed by a review of vectors and matrices in the context of linear equations.  The review will refresh your knowledge of the fundamentals of vectors and of matrix theory, how to perform operations on matrices, and how to solve systems of equations.  After the review, you should be able to understand complex numbers from algebraic and geometric viewpoints to the fundamental theorem of algebra.  Next, we will focus on eigenvalues and eigenvectors.  Today, these have applications in such diverse fields as computer science (Google's PageRank algorithm), physics (quantum mechanics, vibration analysis, etc.), economics (equilibrium states of Markov models), and more.  We will end with the spectral theorem, which provides a decomposition of the vector space on which operators act, and singular-value decomposition, w…

### MA232: Abstract Algebra II

Saylor.org Free Closed [?] Mathematics

This course is a continuation of Abstract Algebra I: we will revisit structures like groups, rings, and fields as well as mappings like homomorphisms and isomorphisms.  We will also take a look at ring factorization, which will lead us to a discussion of the solutions of polynomials over abstracted structures instead of numbers sets.  We will end the section on rings with a discussion of general lattices, which have both set and logical properties, and a special type of lattice known as Boolean algebra, which plays an important role in probability.  We will also visit an important topic in mathematics that you have likely encountered already: vector spaces.  Vector spaces are central to the study of linear algebra, but because they are extended groups, group theory and geometric methods can be used to study them. Later in this course, we will take a look at more advanced topics and consider several useful theorems and counting methods.  We will end the course by studying Galois theoryone of the most im…

### Massively Multivariable Open Online Calculus Course

Starts : 2014-03-14
Coursera Free Mathematics English

M2O2C2 provides a first taste of multivariable differential calculus. By introducing the machinery of linear algebra, this course provides helpful tools for understanding the derivative of a function of many variables.

### Mastering Quantum Mechanics Part 1: Wave Mechanics

Starts : 2016-02-17
edX Free Closed [?] English EdX MITx Physics Science

This physics course offers a sophisticated view of quantum mechanics and its proper mathematical foundation. In this first module of three you will review the basics of wave mechanics and be introduced to the variational principle. You will learn about the technology of spin one-half states and spin operators and get an in-depth look into linear algebra to establish the mathematical foundation necessary to do quantum mechanics. This course concludes by developing the bra-ket notation of Dirac.

To follow this course you will need some basic familiarity with quantum mechanics. You must have seen the Schrödinger equation and studied its solutions for the square well potential, the harmonic oscillator, and the hydrogen atom. You must be proficient in calculus and have some knowledge of linear algebra.

Completing the 3-part Mastering Quantum Mechanics series will give you the necessary foundation to pursue advanced study or research at the graduate level in areas related to quantum mechanics.

Part 1: Wave Mechanics,

Part 2: Quantum Dynamics

The series will follow MIT’s on campus 8.05, the second semester of the three-course sequence on undergraduate quantum mechanics, and will be equally rigorous. 8.05 is a signature course in MIT's physics program and a keystone in the education of physics majors.

Learner Testimonial

I’ve thought long and hard to come up with a better MOOC than this one (I’ve completed 25 of these things over the past 2 years) and can’t do it. 8.05x is #1 and I suspect will stay that way for some time to come.”

“Being an engineering student from India trying to shift to Physics, I am often faced with the requirement to study topics on my own. Very often this has led me to feel inadequate. 8.05x was the perfect opportunity for me to both gain knowledge and evaluate my understanding on a high quality international platform. It has really exceeded my expectations. Now, at the end of fifteen weeks, I feel more confident and hopefully I am more knowledgeable.

### Math 101: College Algebra

Study.com Free Closed [?] Mathematics Algebra College algebra EPA Math

Math 101: College Algebra is designed to be used to prepare you to earn real college credit by passing the College Algebra CLEP Exam . This course covers topics that are included on the exam, including linear equations, functions, graphing, matrices and more. Use it to help you learn what you need to know about algebra topics so you can succeed on the exam.

The algebra instructors are experienced and knowledgeable educators who have put together comprehensive video lessons in categories ranging from absolute value problems to exponentials to the classification of numbers. Each category is broken down into smaller chapters that will cover topics more in-depth. These video lessons make learning fun and interesting. You get the aid of self-graded quizzes and practice tests to allow you to gauge how much you have learned.

### Mathematical Biostatistics Boot Camp 1

Starts : 2015-07-13
Coursera Free Closed [?] Computer Sciences English Biology & Life Sciences Health & Society Mathematics Statistics and Data Analysis

This class presents the fundamental probability and statistical concepts used in elementary data analysis. It will be taught at an introductory level for students with junior or senior college-level mathematical training including a working knowledge of calculus. A small amount of linear algebra and programming are useful for the class, but not required.

### Mathematical Methods for Quantitative Finance

Starts : 2015-06-01
Coursera Free Mathematics English Business & Management Economics & Finance

Mathematical Methods for Quantitative Finance covers topics from calculus and linear algebra that are fundamental for the study of mathematical finance. Students successfully completing this course will be mathematically well prepared to study quantitative finance at the graduate level.

### Mathematical Methods in Nanophotonics

Starts : 2008-02-01
MIT OpenCourseWare (OCW) Free Mathematics Graduate MIT OpenCourseWare

Find out what solid-state physics has brought to Electromagnetism in the last 20 years. This course surveys the physics and mathematics of nanophotonics—electromagnetic waves in media structured on the scale of the wavelength.

Topics include computational methods combined with high-level algebraic techniques borrowed from solid-state quantum mechanics: linear algebra and eigensystems, group theory, Bloch's theorem and conservation laws, perturbation methods, and coupled-mode theories, to understand surprising optical phenomena from band gaps to slow light to nonlinear filters.

Note: An earlier version of this course was published on OCW as 18.325 Topics in Applied Mathematics: Mathematical Methods in Nanophotonics, Fall 2005.

### Mathematics for Materials Scientists and Engineers

Starts : 2005-09-01
MIT OpenCourseWare (OCW) Free Engineering Materials Science and Engineering MIT OpenCourseWare Undergraduate

This course covers the mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from the materials science and engineering core courses (3.012 and 3.014) to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, and fourier analysis.

Users may find additional or updated materials at Professor Carter's 3.016 course Web site.

### Mathematik Online-Kurs - Mathematisch denken!

Starts : 2016-04-08
Iversity Free Closed [?] German Mathematics

#### Kursbeschreibung

Mathematik: das ist Freude am Denken! Und mathematisch denken kann jeder! Wer an diesem Kurs teilnimmt, erhält seine regelmäßige Dosis an meditativen Denkaufgaben, spannenden Knobeleien und mathematischen Einsichten. In den Inhaltsgebieten Arithmetik und Geometrie werden mathematische Denk- und Arbeitsweisen vermittelt, beispielsweise Problemlösen, Begriffe definieren und Sätze finden und beweisen.

#### Was lerne ich in diesem Kurs?

Im ersten Kursblock werden wir uns mit folgenden Fragen befassen: Wie definiert man mathematische Begriffe? Wie findet man eigentlich mathematische Gesetzmäßigkeiten? Und wie beweist man diese? Welche Rolle spielen Annahmen in der Mathematik? Wie baut sich das Gebäude der Mathematik aus Definitionen, Annahmen und Gesetzmäßgikeiten auf? Fragen über Fragen, denen wir uns mit zahlreichen Experimenten widmen.

Im zweiten Kursblock werden wir die Denk- und Arbeitsweisen aus dem ersten Block in verschiedenen Gebieten anwenden und dadurch festigen. In der Geometrie werden wir uns mit der Tätigkeit des Messens und dem Abstandsbegriff, mit Strecken, Halbgeraden und Geraden, mit Ebenen und Halbenenen und mit Winkeln befassen. In der Arithmetik schauen wir uns den Begriff der Teilbarkeit näher an, veranschaulichen Begriffe wie "größter gemeinsamer Teiler" und "kleinstes gemeinsames Vielfaches", untersuchen Primzahlen und Primfaktorzerlegungen und experimentieren mit Stellenwertsystemen.

Im dritten Kursblock befassen wir uns mit grundlegenden mathematischen Konzepten: Was sind Mengen, Relationen und Funktionen? Auch hier werden wir uns den Begriffen und ihren Zusammenhängen mit grundlegenden mathematischen Denk- und Arbeitsweisen nähern. Experimentieren, erforschen, untersuchen, ergründen, Vermutungen anstellen, Vermutungen verwerfen, Vermutungen beweisen.

Im vierten und letzten Kursblock machen wir uns noch einmal an zentrale Gesetzmäßigkeiten der Mathematik. Wie findet man solche Gesetzmäßgikeiten, und wie beweist man sie? In der Geometrie schauen wir uns schicke Sätze am Kreis an, in der Arithmetik nicht weniger schicke Sätze der Zahlentheorie. Mathematik pur, Mathematik anschaulich, Mathematik handgemacht.

#### Welche Vorkenntnisse benötige ich?

Jede/r kann mitmachen, der mathematische Vorkenntnisse aus dem Gymnasium mitbringt. Und wenn Du nicht auf dem Gymnasium warst, aber gerne mitmachen möchtest: Dann trau dich! Man sollte natürlich schon mal mit Geometrie und Algebra zu tun gehabt haben. Vieles wird dann wieder aufgefrischt, denn wir machen dann nicht auf dem Niveau der 12. oder 13. Klasse weiter, sondern bauen die Teilgebiete, in denen wir arbeiten, noch einmal grundlegend auf. Oberstufenwissen zu Analysis und Linearer Algebra ist nicht notwendig!

#### Wie hoch ist der Arbeitsaufwand

Du kannst dich entscheiden, wie aktiv Du dich in den Kurs einbringen möchtest - je nach Interesse und Ehrgeiz!

1) Kiebitze wollen "nur mal gucken" oder mit dem mathematischen Denken erst einmal warm werden. Kiebitze schnuppern jede Woche in den Kurs, schauen sich eins, zwei Videos an und stöbern vielleicht einmal in den weiterführenden Bereichen. Hierdurch bekommen sie einen Einblick, was mathematisches Denken bedeutet, und sie erhalten Impulse, wo man Mathematik auch im Alltag findet und gebrauchen kann. Vielleicht bekommen sie dabei sogar Lust auf mehr! Aufwand: ca. 1-2 Stunden pro Woche

2) Anpacker legen Hand an und erforschen aktiv Mathematik, haben aber keine rechte Lust auf zu viele Formeln. Für Anpacker heißt es: Ärmel hochkrempeln! Im MOOC lernen sie, wie man mathematische Situationen systematisch erforscht, wie man anschauliche Begründungen für mathematische Gesetzmäßgikeiten finden kann, und sie erhalten einen Einblick darin, wie man Abstraktes konkretisiert (und umgekehrt). Sie entwickeln ihre Vorstellungskraft zur Lösung mathematischer Probleme weiter und lernen, Vermutungen anhand konkreter Modelle zu untersuchen. Aufwand: ca. 3-4 Stunden pro Woche

3) Formalisierer geben sich mit der Anschauung nicht zufrieden - sie wollen Formeln sehen! Formalisierer sind Anpacker, die zusätzlich auch noch das Spiel mit abstrakter Symbolsprache lieben. Sie lernen, formale Definitionen zu fassen und formale Beweise zu führen. Natürlich immer basierend auf tragfähigen Vorstellungen, die sie mit den Anpackern teilen! Aufwand: ca. 7-8 Stunden pro Woche

Du möchtest ein Kiebitz in der Arithmetik sein, aber ein Anpacker in der Geometrie? Oder ein Formalisierer in der Arithmetik, aber ein Kiebitz in der Geometrie? Kein Problem - alles ist möglich! So kannst Du deinen individuellen Aufwand selbst wählen und dir diejenigen Inhalte zusammenstellen, die dich interessieren.

#### Erhalte ich ein Zertifikat?

Du erhältst eine Teilnahmebestätigung, wenn du aktiv mitmachst. Wie das genau geht, wird in der ersten Woche erklärt.

### Microeconomic Theory I (Fall 2015)

Starts : 2015-09-01
MIT OpenCourseWare (OCW) Free Business Economics Graduate MIT OpenCourseWare

This half-semester course provides an introduction to microeconomic theory designed to meet the needs of students in an economics Ph.D. program. Some parts of the course are designed to teach material that all graduate students should know. Others are used to introduce methodologies. Students should be comfortable with multivariable calculus, linear algebra, and basic real analysis.

### Multivariable Calculus with Theory

Starts : 2011-02-01
MIT OpenCourseWare (OCW) Free Mathematics MIT OpenCourseWare Undergraduate

This course is a continuation of 18.014. It covers the same material as 18.02 (Multivariable Calculus), but at a deeper level, emphasizing careful reasoning and understanding of proofs. There is considerable emphasis on linear algebra and vector integral calculus.

### Numerical Computation for Mechanical Engineers (Fall 2014)

Starts : 2014-09-01
MIT OpenCourseWare (OCW) Free Engineering Mechanical Engineering MIT OpenCourseWare Undergraduate

This class introduces elementary programming concepts including variable types, data structures, and flow control. After an introduction to linear algebra and probability, it covers numerical methods relevant to mechanical engineering, including approximation (interpolation, least squares and statistical regression), integration, solution of linear and nonlinear equations, ordinary differential equations, and deterministic and probabilistic approaches. Examples are drawn from mechanical engineering disciplines, in particular from robotics, dynamics, and structural analysis. Assignments require MATLAB® programming.

### Numerical Methods Applied to Chemical Engineering (Fall 2006)

Starts : 2006-09-01
MIT OpenCourseWare (OCW) Free Engineering Chemical Engineering Graduate MIT OpenCourseWare

Numerical methods for solving problems arising in heat and mass transfer, fluid mechanics, chemical reaction engineering, and molecular simulation. Topics: numerical linear algebra, solution of nonlinear algebraic equations and ordinary differential equations, solution of partial differential equations (e.g. Navier-Stokes), numerical methods in molecular simulation (dynamics, geometry optimization). All methods are presented within the context of chemical engineering problems. Familiarity with structured programming is assumed. The examples will use MATLAB®.

## Acknowledgements

The instructor would like to thank Robert Ashcraft, Sandeep Sharma, David Weingeist, and Nikolay Zaborenko for their work in preparing materials for this course site.

### Optimization Methods for Business Analytics

Starts : 2016-09-06
edX Free Closed [?] English Business & Management EdX Math MITx

Optimization is the search for the best and most effective solution. In this mathematics course, we will examine optimization through a Business Analytics lens. You will be introduced to the to the theory, algorithms, and applications of optimization. Linear and integer programming will be taught both algebraically and geometrically, and then applied to problems involving data. Students will develop an understanding of algebraic formulations, and use Julia/JuMP for computation. Theoretical components of the course are made approachable, and require no formal background in linear algebra or calculus.

The recommended audience for this course is undergraduates, as well as professionals interested in using optimization software. The content in this course has applications in logistics, marketing, project management, finance, statistics and machine learning.

Most of the course material will be covered in lecture and recitation videos, and only an optional textbook, available at no cost, will be used.

Students interested in the material prior to deciding on course enrollment can visit the MIT Open Courseware version of 15.053 Spring 2013. The topics of the 2013 subject were optimization modeling, algorithms, and theory. As a six week subject, 15.053x covers about half of the material of the 2013 subject. The primary focus of 15.053x is optimization modeling.

### Precalculus

Starts : 2017-05-08
edX Free Closed [?] English ASUx EdX Math

In this college-level Precalculus course, you will prepare for calculus by focusing on quantitative reasoning and functions. You’ll develop the skills to describe the behavior and properties of linear, exponential, logarithmic, polynomial, rational, and trigonometric functions.

Content in this course will be adaptive, allowing you to achieve mastery in a certain concept before moving on to the next. Utilizing the ALEKS learning system, students in this personalized, self-paced course will be instructed on the topics they are most ready to learn while also providing individualized coaching as you move through each topic.

Before taking this course, you should already have a strong understanding of algebraic skills such as factoring, basic equation solving, and the rules of exponents and radicals.

This 3 credit hour course satisfies the Mathematical Studies (MA) general studies requirement at Arizona State University. This course may satisfy a general education requirement at other institutions; however, it is strongly encouraged that you consult with your institution of choice to determine how these credits will be applied to their degree requirements prior to transferring the credit.

### Precalculus Algebra

Canvas.net Free Closed [?] Mathematics Math Precalculus Precalculus Algebra

Students often encounter grave difficulty in calculus if their algebraic knowledge is insufficient. This course is designed to provide students with algebraic knowledge needed for success in a typical calculus course. We explore a suite of functions used in calculus, including polynomials (with special emphasis on linear and quadratic functions), rational functions, exponential functions, and logarithmic functions. Along the way, basic strategies for solving equations and inequalities are reinforced, as are strategies for interpreting and manipulating a variety of algebraic expressions. Students enrolling in the course are expected to have good number sense and to have taken an intermediate algebra course.

### Precorso di calcolo

Starts : 2015-09-08
Iversity Free Closed [?] Italian Mathematics

E' possibile studiare l'intero corso in pochi giorni: il test iniziale di ogni capitolo vi permette di capire su quali argomenti concentrarvi. L'intero corso sarà attivato nello stesso momento, e tutti i materiali saranno disponibili da subito. In questo modo gli iscritti potranno studiare seguendo il loro ritmo e focalizzare l'impegno per rafforzare i propri punti deboli.

Inoltre, per chi si registra al corso durante il periodo di apertura, tutti i materiali resteranno disponibili per ulteriori 6 mesi dopo la chiusura del corso stesso.

#### Riassunto del corso

Il corso consiste in un ripasso delle nozioni di Matematica di base viste nelle Scuole Superiori: insiemi, funzioni, grafici, numeri reali, equazioni e disequazioni, elementi di geometria piana, polinomi, funzioni esponenziali e logaritmi, trigonometria.

#### Obiettivi formativi

Fornire la preparazione per seguire con tranquillità i corsi di matematica al primo anno di Università.

#### Conoscenze richieste

L’algebra e la geometria di base delle scuole superiori.

#### Struttura del corso

L'intero corso sarà attivato nello stesso momento, e tutti i materiali saranno disponibili da subito. In questo modo gli iscritti potranno studiare seguendo il loro ritmo e focalizzare l'impegno per rafforzare i propri punti deboli.
All'inizio di ogni capitolo, ci sarà in quiz per la valutazione del proprio livello. In questo modo è possibile vedere da subito quali sono le proprie lacune e decidere se seguire tutte (o in parte) le video lezioni seguenti.

Capitoli:

Nozioni di base. Insiemi, prodotto cartesiano. Funzioni.

Geometria analitica del piano. Coordinate cartesiane. Grafici di funzioni e simmetrie. La retta. Il cerchio.

Polinomi. Monomi, polinomi, divisione tra polinomi, frazioni di polinomi.

Numeri reali. Numeri reali, valore assoluto, radici di numeri positivi.

Equazioni. Equazioni di primo e secondo grado, equazioni di ordine superiore a 2.

Sistemi di equazioni. Sistemi lineari. Sistemi di primo e secondo grado. Interpretazione grafica.

Disequazioni. Disequazioni di I grado. La regola del prodotto dei segni. Disequazioni di secondo grado. Disequazioni varie (fratte, con modulo/radici).

Esponenziali e logaritmi. Esponenziali. Logaritmi. Applicazione: equazioni e disequazioni con logaritmi/esponenziali.

Trigonometria 1. Le funzioni trigonometriche. Formule di addizione e sottrazione. Formule di prostaferesi.

Trigonometria 2. Funzioni trigonometriche inverse. Equazioni e disequazioni trigonometriche.

#### Università degli Studi di Padova

Fondata nel 1222, l'Università degli Studi di Padova è una delle più antiche e più prestigiose istituzioni accademiche europee. È un'università multidisciplinare che cerca di fornire ai suoi studenti sia un efficace training professionale, sia un solido background culturale. Un titolo di studio acquisito all'Università di Padova è un obiettivo ambizioso, riconosciuto e ricercato sia da studenti sia dal mondo delle imprese.

Se volete sapere di più sull'Univeristà di Padova, visitate il sito web all'indirizzo: http://www.unipd.it

Dipartimento di Matematica

Il Dipartimento di Matematica (DM) è il principale riferimento dell'Ateneo per la matematica sia sul piano della ricerca che su quello della didattica, e ospita al suo interno un gruppo di informatica numericamente limitato, ma di grande valore scientifico. La ricerca spazia in tutti gli ambiti della matematica, della matematica applicata e dell’informatica, proseguendo un'illustre tradizione testimoniata dalla considerazione della comunità scientifica internazionale e recentemente confermata dall’esito della prima Valutazione della Qualità della Ricerca (VQR).

Grazie all’impegno di 63 professori di area matematica, 11 di area informatica e 32 ricercatori, è il dipartimento di riferimento per i Corsi di Laurea di primo e secondo livello in Matematica ed in Informatica; inoltre coordina e parzialmente impartisce gli insegnamenti di matematica in più di 30 Corsi di Studio dell’Ateneo, nei quali la matematica costituisce uno strumento di base nonché una parte fondamentale della formazione scientifica.

Un compito importante del DM è anche la formazione alla ricerca dei giovani. Il DM persegue questo obiettivo ospitando il Corso di Dottorato in Scienze Matematiche e collaborando al Curriculum in Computer Science for societal challenges and innovation del Corso di Dottorato in Brain, Mind and Computer Science.

Maggiori informazioni su sito web http://www.math.unipd.it

### Principles of Electric Circuits | 电路原理

Starts : 2017-02-20
edX Free Closed [?] Engineering English Computer Science EdX Electronics TsinghuaX

Principles of Electric Circuits (20220214x) is one of the kernel courses in the broad EECS subjects. Almost all the required courses in EECS are based on the concepts learned in this course, so it’s the gateway to a qualified EECS engineer.

The main content of this course contains linear and nonlinear resistive circuits, time domain analysis of the dynamic circuits, and the steady state analysis of the dynamic circuits with sinusoidal excitations. Important concepts, e.g. filters, resonance, quiescent point, etc., cutting-edge elements, e.g. MOSFETs and Op Amps, etc., systematic analyzing tools, e.g. node method and phasor method, etc., and real-world engineering applications, e.g. square wave generator and pulse power supply for railgun, etc., will be discussed in depth.

In order to facilitate the learning for students with middle school level, we prepare the necessary knowledge for calculus and linear algebra in week 0. With your effort, we can show you the fantastic view of electricity.

### Quantum Cryptography

Starts : 2017-11-14
edX Free Closed [?] English CaltechX Computer Science DelftX EdX Engineering Physics

How can you tell a secret when everyone is able to listen in? In this course, you will learn how to use quantum effects, such as quantum entanglement and uncertainty, to implement cryptographic tasks with levels of security that are impossible to achieve classically.

This interdisciplinary course is an introduction to the exciting field of quantum cryptography, developed in collaboration between QuTech at Delft University of Technology and the California Institute of Technology.

By the end of the course you will

• Be armed with a fundamental toolbox for understanding, designing and analyzing quantum protocols.
• Understand quantum key distribution protocols.
• Understand how untrusted quantum devices can be tested.
• Be familiar with modern quantum cryptography – beyond quantum key distribution.

This course assumes a solid knowledge of linear algebra and probability at the level of an advanced undergraduate. Basic knowledge of elementary quantum information (qubits and simple measurements) is also assumed, but if you are completely new to quantum information additional videos are provided for you to fill in any gaps.

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