--- tags: mth225, learning-targets --- # MTH 225 Fall 2021 Learning Targets ## Module 1: Computer Arithmetic * CA.1 (**CORE**) I can represent an integer in base 2, 8, 10, and 16 and represent a negative integer in base 2 using two’s complement notation. * CA.2 I can perform addition, subtraction, multiplication, and division in binary. ## Module 2: Logic * L.1 (**CORE**) I can identify the parts of a conditional statement and write the negation, converse, and contrapositive of a conditional statement. * L.2 I can construct truth tables for propositions involving two or three variables and use truth tables to determine if two propositions are logically equivalent. * L.3 I can identify the truth value of a predicate, determine whether a quantified predicate is true or false, and state the negation of a quantified statement. ## Module 3: Sets and Functions * SF.1 (**CORE**) I can represent a set in roster notation and set-builder notation; determine if an object is an element of a set; and determine set relationships (equality, subset). * SF.2 I can perform operations on sets (intersection, union, complement, Cartesian product), determine the cardinality of a set, and write the power set of a finite set. * SF.3 (**CORE**) I can determine whether or not a given relation is a function; determine the domain, range, and codomain of a function; and find the image and preimage of a point using a function. * SF.4 I can determine whether a function is injective, surjective, or bijective. * SF.5 I can evaluate special computer science functions: floor, ceiling, factorial, DIV, and MOD (`%`). ## Module 4: Combinatorics * C.1 (**CORE**) I can use the additive and multiplicative principles and the Principle of Inclusion and Exclusion to formulate and solve counting problems. * C.2 (**CORE**) I can calculate a binomial coefficient and correctly apply the binomial coefficient to formulate and solve counting problems. * C.3 I can count the number of permutations of a group of objects and the number of $k$-permutations from a set of $n$ objects. * C.4 I can use the "stars and bars" method to count the number of ways to distribute objects among a group. ## Module 5: Recursion and Induction * RI.1 (**CORE**) I can generate several values in a sequence defined using a closed-form expression or using recursion. * RI.2 I can use sigma notation to rewrite a sum and determine the sum of an expression given in sigma notation. * RI.3 I can find closed-form and recursive expressions for arithmetic and geometric sequences. * RI.4 I can determine a recurrence relation for a given recursive sequence and check whether a proposed solution to a recurrence relation is valid. * RI.5 I can solve a second-order linear homogeneous recurrence relation using the characteristic root method. * RI.6 (**CORE**) Given a statement to be proven by mathematical induction, I can state and prove the base case, state the inductive hypothesis, and outline the proof.
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Robert Talbert
Professor of Mathematics, Grand Valley State University. Writer (http://rtalbert.org, http://rtalbert.org/book), speaker, researcher.
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MTH 201-04: Calculus, Winter 2021

:::info Welcome to MTH 201! I'm Dr. Robert Talbert, Professor of Mathematics, and I am grateful that you are signed up for the course and am looking forward to working with you this semester. ::: What's MTH 201 all about? MTH 201 is a first course in Calculus, which is all about modeling and understanding change. Change is maybe the most important facet of the world around us, and we care about it more than we realize. For example, we care a lot about the number of Covid-19 cases in our community, but we might care even more about how fast the number of cases is changing (either up or down). In MTH 201, you'll learn the mathematical language of change and apply it to models that you build to draw conclusions, make predictions, and give meaningful answers to real problems. MTH 201 goes beyond just computation. In MTH 201, you'll build skills with understanding complex concepts, communicating those concepts and the meaning of your results to appropriate audiences, using professional tools to help you in your work, and practice working with others to improve your learning (and theirs). These are valuable skills no matter where you go next. Success in this course doesn't come easy, and you can expect to be pushed and stretched intellectually. But the struggle you experience is normal and healthy, a sign of growth and that you are doing things the right way. And you will receive tireless support from me and your classmates in the process. Above all, my top priority is to support you in your work and help you succeed.

11/11/2023
Miniproject 8

Initial due date: Sunday, April 9 at 11:59pm ET Overview Our final miniproject reaches back into linear algebra to look at diagonalizable matrices and their uses in solving systems of differential equations. Prerequisites: You'll need to be able to solve basic systems of differential equations and find the eigenvalues and eigenvectors for a small matrix. You'll also need a basic comfort level with concepts of linear independence and matrix arithmetic from earlier in the course. Background This entire problem comes from Section 3.9.1 in your textbook. Here is a rephrased version of the introduction to that section.

3/29/2023
Miniproject 7

Initial due date: Sunday, April 9 at 11:59pm ET Overview This miniproject will teach you about the Runge-Kutta method, a standard numerical solution technique for differential equations. Prerequisites: A strong grasp of Euler's Method for single DE's is needed. You will also need to be comfortable using a spreadsheet. Miniproject 6 (Euler's Method for systems) is also recommended. Background A description of the Runge-Kutta method along with an example is given in this tutorial. Read it carefully and make sure you can work along with the example before proceeding.

3/29/2023
Miniproject 6

Initial due date: Sunday, April 9 at 11:59pm ET Overview This miniproject introduces a version of Euler's Method as a numerical solution technique for systems. Prerequisites: You will need to be comfortable with using Euler's method for single differential equations. You'll also benefit from some familiarity with spreadsheets or Python in order to automate the calculations. Background This tutorial gives you the background you need for this assignment. Please read it and make sure you understand the concepts and the example: https://github.com/RobertTalbert/linalg-diffeq/blob/main/assignments/Euler's_Method_for_Systems.ipynb

3/22/2023
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