This lesson is part of Software Carpentry workshops and teach an introduction to plotting and programming using python. This lesson is an introduction to programming in Python for people with little or no previous programming experience. It uses plotting as its motivating example, and is designed to be used in both Data Carpentry and Software Carpentry workshops. This lesson references JupyterLab, but can be taught using a regular Python interpreter as well. Please note that this lesson uses Python 3 rather than Python 2.

Module 1 sets the stage for expanding students' understanding of transformations by exploring the notion of linearity.  This leads to the study of complex numbers and linear transformations in the complex plane.  The teacher materials consist of the teacher pages including exit tickets, exit ticket solutions, and all student materials with solutions for each lesson in Module 1.

Module 2 extends the concept of matrices introduced in Module 1.  Students look at incidence relationships in networks and encode information about them via high-dimensional matrices.  Matrix properties are studied as well as the role of the zero and identity matrices.  Students then use matrices to study and solve higher order systems of equations.  Vectors are introduced, and students study the arithmetic of vectors and vector magnitude.  The module ends as students program video games using matrices and vectors.

Students revisit the fundamental theorem of algebra as they explore complex roots of polynomial functions.  They use polynomial identities, the binomial theorem, and Pascal’s Triangle to find roots of polynomials and roots of unity. Students compare and create different representations of functions while studying function composition, graphing functions, and finding inverse functions.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

This module revisits trigonometry that was introduced in Geometry and Algebra II, uniting and further expanding the ideas of right triangle trigonometry and the unit circle.  New tools are introduced for solving geometric and modeling problems through the power of trigonometry.  Students explore sine, cosine, and tangent functions and their periodicity, derive formulas for triangles that are not right, and study the graphs of trigonometric functions and their inverses.

In this module, students build on their understanding of probability developed in previous grades.  In Topic A the multiplication rule for independent events introduced in Algebra II is generalized to a rule that can be used to calculate probability where two events are not independent.  Students are also introduced to three techniques for counting outcomes.  Topic B presents information related to random variables and discrete probability distributions.  Topic C is a capstone topic for this module, where students use what they have learned about probability and expected value to analyze strategies and make decisions in a variety of contexts.

(Nota: Esta es una traducción de un recurso educativo abierto creado por el Departamento de Educación del Estado de Nueva York (NYSED) como parte del proyecto "EngageNY" en 2013. Aunque el recurso real fue traducido por personas, la siguiente descripción se tradujo del inglés original usando Google Translate para ayudar a los usuarios potenciales a decidir si se adapta a sus necesidades y puede contener errores gramaticales o lingüísticos. La descripción original en inglés también se proporciona a continuación.)

El módulo 2 extiende el concepto de matrices introducidas en el módulo 1. Los estudiantes analizan las relaciones de incidencia en las redes y codifican información sobre ellas a través de matrices de alta dimensión. Se estudian las propiedades de la matriz, así como el papel de las matrices cero y de identidad. Luego, los estudiantes usan matrices para estudiar y resolver sistemas de ecuaciones de orden superior. Se introducen vectores y los estudiantes estudian la aritmética de los vectores y la magnitud del vector. El módulo termina cuando los estudiantes programan videojuegos usando matrices y vectores.

English Description:
Module 2 extends the concept of matrices introduced in Module 1.  Students look at incidence relationships in networks and encode information about them via high-dimensional matrices.  Matrix properties are studied as well as the role of the zero and identity matrices.  Students then use matrices to study and solve higher order systems of equations.  Vectors are introduced, and students study the arithmetic of vectors and vector magnitude.  The module ends as students program video games using matrices and vectors.

(Nota: Esta es una traducción de un recurso educativo abierto creado por el Departamento de Educación del Estado de Nueva York (NYSED) como parte del proyecto "EngageNY" en 2013. Aunque el recurso real fue traducido por personas, la siguiente descripción se tradujo del inglés original usando Google Translate para ayudar a los usuarios potenciales a decidir si se adapta a sus necesidades y puede contener errores gramaticales o lingüísticos. La descripción original en inglés también se proporciona a continuación.)

Los estudiantes vuelven a visitar el teorema fundamental del álgebra mientras exploran raíces complejas de funciones polinomiales. Utilizan identidades polinomiales, el teorema binomial y el triángulo de Pascal para encontrar raíces de polinomios y raíces de la unidad. Los estudiantes comparan y crean diferentes representaciones de funciones mientras estudian composición de funciones, gráficos de funciones y encuentran funciones inversas.

Encuentre el resto de los recursos matemáticos de Engageny en https://archive.org/details/engageny-mathematics.

English Description:
Students revisit the fundamental theorem of algebra as they explore complex roots of polynomial functions.  They use polynomial identities, the binomial theorem, and Pascal’s Triangle to find roots of polynomials and roots of unity. Students compare and create different representations of functions while studying function composition, graphing functions, and finding inverse functions.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

(Nota: Esta es una traducción de un recurso educativo abierto creado por el Departamento de Educación del Estado de Nueva York (NYSED) como parte del proyecto "EngageNY" en 2013. Aunque el recurso real fue traducido por personas, la siguiente descripción se tradujo del inglés original usando Google Translate para ayudar a los usuarios potenciales a decidir si se adapta a sus necesidades y puede contener errores gramaticales o lingüísticos. La descripción original en inglés también se proporciona a continuación.)

Este módulo revisa la trigonometría que se introdujo en la geometría y el álgebra II, uniendo y ampliando aún más las ideas de la trigonometría del triángulo recto y el círculo unitario. Se introducen nuevas herramientas para resolver problemas geométricos y de modelado a través del poder de la trigonometría. Los estudiantes exploran funciones sinuso, coseno y tangentes y su periodicidad, derivan fórmulas para triángulos que no son correctos y estudian los gráficos de las funciones trigonométricas y sus inversos.

English Description:
This module revisits trigonometry that was introduced in Geometry and Algebra II, uniting and further expanding the ideas of right triangle trigonometry and the unit circle.  New tools are introduced for solving geometric and modeling problems through the power of trigonometry.  Students explore sine, cosine, and tangent functions and their periodicity, derive formulas for triangles that are not right, and study the graphs of trigonometric functions and their inverses.

In the first half of this module, students identify measurable attributes of objects in terms of length, weight, and capacity.  Students learn words such as small, big, short, tall, empty, full, heavy, and light so that they will have the vocabulary needed to describe objects (PK.MD.1).  The comparison of length, weight, and capacity naturally leads to discussions about quantity and number.  In the second half, measurement is connected to quantity as students reason if there are enough, more than, less than, or the same number of objects in a set using matching and counting strategies (PK.CC.5).  Comparing concrete sets leads to comparing quantities and abstract numbers.  Children will also focus on identifying first and last in quantities up to 5 and 10 in different configurations (PK.CC.6).

Module 5 is the culmination of children's work with number in the Pre-K year.  Throughout Modules 1 and 3, they had extensive counting experiences with numbers 0-10.  In Module 4, they examined the relationships between numbers 1-5 through comparison.  In Module 5, children transition from the comparative concept of more (4 apples is more than 1 apple) to the concept of addition (3 apples and 1 more apple make 4 apples).  They are ready to begin work with operations, focusing on addition and subtraction stories with numbers 1 to 5.  Students will also learn to write numerals 0-5 and explore patterns in this final module.

Module 1 capitalizes on the energy and excitement young students have as they enter their first day of Pre-K by providing a playful and active yet carefully sequenced structure through which children progress.  In this module, we set up a friendly learning environment in which children have sustained interaction with four core ideas, collectively referred to as the number core:  rote counting (the number word list), one-to-one correspondence (one object paired with one number word), cardinality (how many in a set), and written numerals.  Throughout the module, children have experiences that help them make critical connections between these four understandings.

In Module 2, in the context of classroom play, children learn to identify, describe, sort, compare, and create two-dimensional (2-D) and three-dimensional (3-D) shapes and objects. Children develop vocabulary to describe the relative position of objects (e.g., top, bottom, up, down, in front of, behind, over, under, and next to), building foundational spatial reasoning abilities. In Module 1, students developed an understanding of numbers to 5. In Module 2, students practice these counting skills in the context of geometry (counting sides, corners, a group of triangles, etc.).

Module 3 challenges students to build on their work with numbers through 5 to make sense of and count groups of 0, 6, 7, 8, 9, and 10 objects. Students also continue their work with the number core in the following ways (PK.CC.1–4): Rote counting (the number word list up to 15); one-to-one correspondence (one object paired with one number word from 0 to 10); cardinality (how many in a set of up to 10 objects); andnumber recognition (matching written numerals 0, 6, 7, 8, 9, and 10 to quantities). Throughout the module, children participate in engaging experiences that help them make critical connections between these four understandings.

In order to give Introductory Geology (Physical Geology) undergraduate non-majors students experience and confidence in using basic algebra to calculate very simple stream flow properties, we use a prework assignment prior to the Rivers and Streams Lab. Prework is a worksheet assigned 2 weeks in advance, which asks students to calculate velocity and discharge as well as unit conversions and calculations of stream load. The questions are put into the context of activities they completed earlier in the semester during visits to the stream (on campus) so questions are relevant to their previous experiences. The prework timeframe gives students the opportunity to seek extra help from their instructor prior to the lab period in which they will make additional measurements, similar calcualations and interpretations of their data.

(Note: this resource was added to OER Commons as part of a batch upload of over 2,200 records. If you notice an issue with the quality of the metadata, please let us know by using the 'report' button and we will flag it for consideration.)

Explain how a density function is used to find probabilities involving continuous random variables.

Learning Objective: Apply probability rules in order to find the likelihood of an event.

The best way to learn how to program is to do something useful, so this introduction to MATLAB is built around a common scientific task: data analysis. Our real goal isn’t to teach you MATLAB, but to teach you the basic concepts that all programming depends on. We use MATLAB in our lessons because: we have to use something for examples; it’s well-documented; it has a large (and growing) user base among scientists in academia and industry; and it has a large library of packages available for performing diverse tasks. But the two most important things are to use whatever language your colleagues are using, so that you can share your work with them easily, and to use that language well.

The best way to learn how to program is to do something useful, so this introduction to Python is built around a common scientific task: data analysis. Arthritis Inflammation We are studying inflammation in patients who have been given a new treatment for arthritis, and need to analyze the first dozen data sets of their daily inflammation. The data sets are stored in comma-separated values (CSV) format: each row holds information for a single patient, columns represent successive days. The first three rows of our first file look like this: 0,0,1,3,1,2,4,7,8,3,3,3,10,5,7,4,7,7,12,18,6,13,11,11,7,7,4,6,8,8,4,4,5,7,3,4,2,3,0,0 0,1,2,1,2,1,3,2,2,6,10,11,5,9,4,4,7,16,8,6,18,4,12,5,12,7,11,5,11,3,3,5,4,4,5,5,1,1,0,1 0,1,1,3,3,2,6,2,5,9,5,7,4,5,4,15,5,11,9,10,19,14,12,17,7,12,11,7,4,2,10,5,4,2,2,3,2,2,1,1 Each number represents the number of inflammation bouts that a particular patient experienced on a given day. For example, value “6” at row 3 column 7 of the data set above means that the third patient was experiencing inflammation six times on the seventh day of the clinical study. So, we want to: Calculate the average inflammation per day across all patients. Plot the result to discuss and share with colleagues. To do all that, we’ll have to learn a little bit about programming.