Math 136 notes

MATH is a foundational course for students in the Faculty, yet too many were struggling to learn the material.

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Modifications to high school curricula required a different strategy for the delivery of this course. The time had come to try something new to improve student outcomes and their intellectual stamina in learning mathematics. In the fall term, 15 instructors led by Professor J. Pretti implemented a different version of the course for first-year students. All of this was accomplished while maintaining the academic rigour students expect at Waterloo.

MATH is centered on proof, the defining property of mathematics. Proof defines the transition from high school to university mathematics. It must be thoroughly understood for students to be successful in their upper year math courses. Classes were smaller. Instead of students, MATH was offered in sections of just 60 students. Instructors got to know their students by name, and provide more one-on-one support during office hours. Smaller classes also helped the students to better connect and help each other.

In-class participation increased, along with attendance. Instructors found that being able to call on the students by name made them more comfortable offering answers. The classes met four times a week with their primary instructor, instead of the previous model of three times a week plus an hour tutorial with a teaching assistant. Lectures were designed so that there was time devoted to working through and discussing in-class exercises. This transition meant more preparation time for the instructors, but they were happy to see that the new approach worked.

The students were pushed further, in terms of the difficulty of assignments and exams, yet showed a more solid understanding of the material. Instead of just listening to an instructor present the course material while they took notes, the students worked through problems in class. Spending this in-class time practicing proofs helps instill confidence.

When students believe they can do it, they enjoy the material more and are ready to tackle even the most challenging assignment questions and exams. There were over 10, posts over the term for this course alone. They were also chiming in to support classmates with questions, and offering insightful comments on the course material. Increasing student engagement and active learning with these changes to MATH was a very successful experiment.

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Not only were the grades better overall, but instructors noted that students seemed to show more interest in the material and to enjoy the course more. MATH instructors were pleased with the outcome of the course delivery transition, and they credit Professor J.

His collegiality and organization were noted by his colleagues, who also appreciated his trouble-shooting and clear direction. Support Mathematics. Department of Combinatorics and Optimization. Department of Statistics and Actuarial Science.

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples.

Our main campus is situated on the Haldimand Tract, the land promised to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Indigenous Initiatives Office.CS builds on the techniques and patterns that you learned in CS The primary focus of the course is the design, analysis and implementation of fundamental algorithms and data structures.

This necessitates the use of computational models for both Scheme and C that more closely resemble what happens in actual implementations. The goal of CS is to give students the tools and concepts necessary to solve computational problems in a robust, efficient and verifiable manner.

You can find the handbook description of the course here. All announcements will be made through piazza. We will link to major announcements here. With the exceptions of reading week and midterm week, each week in CS will follow a similar structure. Make sure that you do not miss any due dates:. Home This is the homepage for CS Fall Major Announcements All announcements will be made through piazza.

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Lecture slides for Section 6 has been released. Tutorial 3 is now available on our YouTube channel. Lecture slides for Section 5 has been released. Tutorial 2 is available on our YouTube channel. Lecture slides for Section 4 has been released. Lecture slides for Section 3 and Quiz 3 have been released.Detailed course offerings Time Schedule are available for Autumn Quarter Includes linear equations and models, linear systems in two variables, quadratic equations, completing the square, graphing parabolas, inequalities, working with roots and radicals, distance formula, functions and graphs, exponential and logarithmic functions.

Course awarded as transfer equivalency only. Consult the Admissions Equivalency Guide website for more information. Assumes no previous experience in algebra. Open only to students [1] in the Educational Opportunity Program or [2] admitted with an entrance deficiency in mathematics.

Offered: A. Prerequisite: minimum grade of 2. Offered: AW. Open only to students who have completed MATH Offered: WSp. Consult the Admissions Exams for Credit website for more information.

Algebraic and graphical manipulations to solve problems. Exponential and logarithm functions; various applications to growth of money. Offered: AWS. Techniques of differentiation and integration. Application to problem solving. Credit does not apply toward a mathematics major. Content varies and must be individually evaluated. MATH Precalculus 5 NW Basic properties of functions, graphs; with emphasis on linear, quadratic, trigonometric, exponential functions and their inverses.

Emphasis on multi-step problem solving. Offered: AWSpS. Emphasizes differential calculus. Emphasizes applications and problem solving using the tools of calculus. Emphasizes integral calculus. Prerequisite: either minimum grade of 2. Introduction to Taylor polynomials and Taylor series, vector geometry in three dimensions, introduction to multivariable differential calculus, double integrals in Cartesian and polar coordinates.

Prerequisite: either a minimum grade of 2. First year of a two-year accelerated sequence.Following toggle tip provides clarification. Topics include orthogonal and unitary matrices and transformations; orthogonal projections; the Gram-Schmidt procedure; and best approximations and the method of least squares.

Inner products; angles and orthogonality; orthogonal diagonalization; singular value decomposition; and other applications will also be explored. In this module, we will look at the fundamental subspaces of a matrix and of a linear mapping, and prove some useful results. Part of the purpose of this module is to help review and recall many of the concepts from Linear Algebra I that are needed for this course. In this module, we will extend the concept of a linear mapping from R n to R m to linear mappings from a vector space V to a vector space W.

It may be helpful to briefly review linear mappings from R n to R mwhich includes the matrix of a linear mapping and diagonalization. Previously, we studied the important concepts of length, orthogonality, and projections.

Since these concepts are so amazingly useful in R nin this module, we will generalize all of these concepts to general vector spaces.

To do this, we will need to first generalize the idea of the dot product in R n to the concept of an inner product on a general vector space. This will lead us to an extremely important theorem in linear algebra. Finally, we will use the theory we developed in this module to actually look at a real-world application, called the method of least squares. In this module, we will use the theory we have previously developed to extend the idea of diagonalization to something even better: orthogonal diagonalization.

This will lead us to the extremely useful and important topic of quadratic forms. Finally, using all of the theory we have developed, we will look at how to mimic diagonalization for non-square matrices.

In this module, we are going to revisit many concepts covered previous, now allowing the use of complex numbers. We will see that much of the theory remains the same, but there will be some differences.

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Moreover, we will see that quite a lot of the computations will now be a little more complex. Toggle navigation System Homepage. Linear Algebra 2 Class Homepage. Fundamental Subspaces In this module, we will look at the fundamental subspaces of a matrix and of a linear mapping, and prove some useful results. Lesson: Fundamental Subspaces of a Matrix. Lesson: Bases for Fundamental Subspaces. Quiz: Fundamental Subspaces of Matrix.

math 136 notes

Linear Mappings In this module, we will extend the concept of a linear mapping from R n to R m to linear mappings from a vector space V to a vector space W. Lesson: Linear Mappings. Quiz: General Linear Mappings.If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Donate Login Sign up Search for courses, skills, and videos.

math 136 notes

Early math Learn early elementary math—counting, shapes, basic addition and subtraction, and more. Counting : Early math. Addition and subtraction intro : Early math. Place value tens and hundreds : Early math. Addition and subtraction within 20 : Early math. Addition and subtraction within : Early math. Measurement and data : Early math. Geometry : Early math. Kindergarten Learn kindergarten math—counting, basic addition and subtraction, and more.

Addition and subtraction : Kindergarten. Measurement and geometry : Kindergarten. Addition and subtraction : 1st grade. Measurement, data, and geometry : 1st grade. Place value : 2nd grade. Add and subtract within : 2nd grade. Add and subtract within 1, : 2nd grade. Money and time : 2nd grade.Math is the second semester of the Math sequence for students studying Life Sciences or Social Sciences. Math is designed specifically for students who want a second semester of calculus for their technical background, but who do not intend to take further courses in Calculus or Differential Equations.

Therefore, Math offers a mixture of traditional Calculus II topics and of additional topics—such as mulitivariate functions and constrained optimization using Lagrange multipliers—that students are likely to meet in scientific applications.

Life Sciences majors may also take Math to fulfill their requirement of a second semester Calculus course. To decide which course they would prefer, Life Sciences majors should also visit the Math web page.

To include the additional material described above, Math excludes many topics that are needed in a third semester calculus course such as Math The same applies to Math Students who may wish to take Math should follow Math with Mathnot Math and not Math This applies to students in certain programs in the Life Sciences in particular, Molecular Biology and Biochemistrywhich require Math More information on the transition from Math to Math can be found on the web page Mathematics Placement Advice.

Smith, M. Strauss and M. Here is the current departmental syllabus for the course. Your instructor will supply his or her own version of this syllabus. Sosa Fall Prof.

D in senior year

Buch Spring Prof. Noone Fall Prof. Irvine, Venugopalan Fall : Prof. Herschkorn Spring Prof. Rainsford Fall Prof. Rainsford Spring Prof. Buhl Spring Profs.

math 136 notes

Ocone and Gundy Fall ?? Fall Prof. Goldstein Spring ??

Textbook Notes for MATH136 at University of Waterloo (UW)

Spring Dov Chelst Fall Prof. Text: Larson Hoestler Edwards. New Text Beginning Spring : Profs.The concepts included are limits, derivatives, antiderivatives and definite integrals. These concepts will be applied to solve problems of rates of change, maximum and minimum, curve sketching and areas. The classes of functions used to develop these concepts and applications are: polynomial, rational, trigonometric, exponential and logarithmic. An introduction to applications of algebra to business, the behavioural sciences, and the social sciences.

Topics will be chosen from linear equations, systems of linear equations, linear inequalities, functions, set theory, permutations and combinations, binomial theorem, probability theory. An introduction to applications of calculus in business, the behavioural sciences, and the social sciences.

The models studied will involve polynomial, rational, exponential and logarithmic functions. The major concepts introduced to solve problems are rate of change, optimization, growth and decay, and integration.

MATH136 Chapter 1-11: Wolczuk LinearAlgebra Solutions 136.pdf

Systems of linear equations. Matrix algebra.

math 136 notes

Introduction to vector spaces. Vectors in 2- and 3-space and their geometry. Linear equations, matrices and determinants. Eigenvalues and diagonalization. Complex numbers. Functions: review of polynomials, exponential, logarithmic, trigonometric. Operations on functions, curve sketching. Trigonometric identities, inverse functions. Derivatives, rules of differentiation.

Mean Value Theorem, Newton's Method. Indeterminate forms and L'Hopital's rule, applications. Integrals, approximations, Riemann definite integral, Fundamental Theorems. Applications of the integral. Functions of engineering importance; review of polynomial, exponential, and logarithmic functions; trigonometric functions and identities.

Inverse functions logarithmic and trigonometric.

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Limits and continuity. Derivatives, rules of differentiation; derivatives of elementary functions. Applications of the derivative, max-min problems, Mean Value Theorem. Antiderivatives, the Riemann definite integral, Fundamental Theorems. Methods of integration, approximation, applications, improper integrals.

Methods of integration: by parts, trigonometric substitutions, partial fractions; engineering applications, approximation of integrals, improper integrals. Linear and separable first order differential equations, applications. Parametric curves and polar coordinates, arc length and area. Infinite sequences and series, convergence tests, power series and applications.

Taylor polynomials and series, Taylor's Remainder Theorem, applications.


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