mathematical problem solving course

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• Prof. Yufei Zhao

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• Mathematics

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Learning resource types, mathematical problem solving (putnam seminar), course description.

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18.A34 Mathematical Problem Solving (Putnam Seminar)

Fall 2023, MIT

[Dropbox (schedule & homework PDFs)] [Canvas]

Class meetings: Mondays and Wednesdays 1–2pm, room 2-132

Instructor: Prof. Yufei Zhao

Undergraduate Assistants (UA): Mark Saengrungkongka and Tomasz Slusarczyk

• For quick questions, ask me after class
• Include both UAs in all class related communication, including everything homework related (submission, extensions, grading, etc.)
• Begin your email subject line with “[18.A34]”

Course description and policies

• A first-year undergraduate seminar. Seminar participants are selected through the First-year Advising Selection process. Unfortunately I cannot add additional students.
• Intended for students with previous math competition experience
• Lectures highlight problem solving techniques as well as connections to further mathematics
• Emphasis on developing mathematical communication skills, including blackboard presentation and proof writing
• Discussions of academic and career topics relevant for students from a math competition background
• All registered students will be required to participate in the Putnam competition. Sign up information will be announced.

Class format

• Lectures are open to all MIT students.
• Each class starts with a brief discussion, followed by student blackboard presentations of homework solutions
• Active participation is expected.
• Students should volunteer to present via a Google Form sent out in Canvas
• 10-minute time limit per presentation. Feel free to skip routine calculations and details
• In small groups lead by a UA, students practice giving presentations and receive feedback from the UA
• Attendance is required roughly once every two weeks for each student
• See Canvas announcements
• Please notify me in advance if you cannot make it to class (e.g., due to illness).
• Too many unexcused absences is cause for concern and may lead to a non-passing grade.
• Non-registered MIT students are welcome to attend sessions below marked “lecture” but not other sessions
• Pass/Fail. Based on homework and participation.
• Homework will be graded on correctness and presentation.

Students needing support should consider reaching out to Student Support Services (S 3 ) or Student Disability Services .

Schedule and due dates

SS = Supplementary set

♡ = recommended problems

• W 9/6 Class introduction
• M 9/11 Discussion & Presentations. Due: Probability & SS1
• W 9/13 Lecture by Yufei Zhao
• M 9/18 Discussion & Presentations. Due: Hidden independence and uniformity & SS2
• W 9/20 Lecture by Mehtaab Sawhney
• M 9/25 Discussion & Presentations. Due: Inequalities & SS3
• W 9/27 Lecture by Mingyang Deng
• M 10/2 Discussion & Presentations. Due: Combinatorial configurations & SS4
• W 10/4 Lecture by Luke Robitaille
• M 10/9 No class: Indigenous Peoples Day
• W 10/11 Discussion & Presentations. Due: Congruences and divisibility & SS5
• M 10/16 Discussion & Presentations. Due: Generating functions & SS6
• W 10/18 Lecture by Dain Kim
• M 10/23 Discussion & Presentations. Due: Polynomials & SS7
• W 10/25 Lecture by Ashwin Sah
• M 10/30 Discussion & Presentations. Due: Analysis & SS8
• W 11/1 Lecture by Edward Wan
• M 11/6 Discussion & Presentations. Due: Sums and integrals ( notes ) & SS9
• W 11/8 Lecture by Papon Lapate
• M 11/13 Discussion & Presentations. Due: Abstract algebra & SS10
• W 11/15 Lecture by Allen Liu
• M 11/20 Discussion & Presentations. Due: Linear algebra & SS11
• W 11/22 Discussion & Presentations (on any assigned problem)
• M 11/27 Discussion & Presentations: Putnam 2021
• W 11/29 Discussion & Presentations: Putnam 2022
• Saturday 12/2 Putnam Competition
• M 12/4 Discussion & Presentations: Putnam 2023 A
• W 12/6 Discussion & Presentations: Putnam 2023 A
• M 12/11 Discussion & Presentations: Putnam 2023 B
• W 12/13 Discussion & Presentations: Putnam 2023 B

Past Putnam problems: Putnam Archive

• Each problem set contains a long list of problems
• You are encouraged to try many problems, but please only hand in your three best solutions (do not submit more than three). If you don’t know which ones to start, try the ones marked by ♡ first.
• At least two problems should come from the topic set, i.e., at most one problem can come from the supplementary problem set.
• Do not hand in supplementary problems rated strictly less than [2]; these are too easy.
• For multi-part problems, you may decide what counts as “one solution”, as long as it is reasonable (i.e., not too trivial).
• If you wish to get a head start on later problem sets, you can check out the material from previous semesters (see links at the bottom). This year’s problem sets will likely be mostly the same, although there could be minor changes and re-numbering.
• Begin each solution on a new page
• State your sources at the top of each problem (even if you worked independently); see below
• Homework must be submitted on Gradescope (accessible from Canvas) by 1pm, before the beginning of the class meeting, preferably earlier.
• Submissions should be typed in LaTeX and submitted as PDF. Reach out to the UAs for help with LaTeX if needed.
• Homework will be graded similarly to the Putnam competition.
• Problems range widely in difficulty. You are encouraged to challenge yourself and submit your best solutions.
• Do not worry if a problem set covers an area of mathematics you have not yet formally learned (e.g., algebra, analysis). Try your best.
• Non-registered students may not hand in solutions.

Late policy

• Late submissions will not be accepted without a valid excuse.
• If you need an extension for valid excuses (e.g., unanticipated health or family issues), please email the UAs and me in advance or have S 3 send us a message. Let us know how many days extension you need.
• My policy is to not grant extension based on forseeable circumstances including other academic workload, extracurriculars, and poor study habits.

Acknowledging collaborators and sources

It is required to acknowledge your sources (even if you worked independently)

• At the beginning of the submission for each problem , write Collaborators and sources: followed by a list of collaborators and sources consulted (people, books, papers, websites, software, etc.), or write none if you did not use any such resources.
• Failure to acknowledge will result in an automatic 1pt penalty per problem.
• Acceptable uses of resources include: looking up a standard theorem/formula/technique; using Wolfram Alpha/Mathematica/Python for a calculation
• You may NOT intentionally look up (or ask from others) solutions to homework problems prior to solving the problems yourselves. Once you have solved a problem, it is fine to seek and learn alternate solutions.

Collaborations

• You are encouraged to first work on the homework problems yourself before seeking collaboration.
• Meaningful collaboration is allowed if it helps with your learning (e.g., solving a problem together)
• Unacceptable practices include: “dividing up” the problems among a group and then distributing the solutions; asking for a solution from a friend.
• You must write up your own solutions.

Intentional violations of the above policies may be considered academic dishonesty/misconduct.

Additional resources

You may find the following optional resources helpful for additional preparation. Some resources may be available electronically from MIT Library .

Previous Putnam problems and solutions

• Putnam archive by Kedlaya
• The William Lowell Putnam Mathematical Competition 2001–-2016: Problems, Solutions, and Commentary by Kedlaya, Kane, Kane, and O’Dorney
• The William Lowell Putnam Mathematical Competition 1985–2000: Problems, Solutions, and Commentary by Kedlaya, Poonen, and Vakil

Additional books helpful for preparation

• Problem-Solving Through Problems by Larson
• Putnam and Beyond by Gelca and Andreescu

Previous course homepage from 2017 , 2018 , 2019 , 2020 , 2021 , 2022 .

Following toggle tip provides clarification

Problem Solving and Mathematical Discovery

• Class Homepage

This courseware helps students to become better problem solvers. Students will learn about roughly a dozen problem techniques (such as Draw a useful diagram, Find a pattern, Consider cases) and explicitly look at problem solving in a number of major topic areas (such as Number Theory, Counting, Geometry). None of the problems presented in this course uses material beyond that covered in the Advanced Functions and Pre-Calculus courseware. The majority of the problems discussed would be accessible to strong and motivated students in Grades 10 and 11.

Introduction

Equations, algebra, and functions, number theory, problem solving wrap-up, additional resources.

In this unit we solve one difficult problem and some easier variations of the problem. Through the development of the solutions we begin to think about problem solving strategies and techniques that will be formalized in the next unit.

Welcome video

Includes Problems 1-5

In this unit we explore a variety of problem solving techniques.

We apply some of the techniques learned in the previous unit to solve problems involving equations, algebra, and functions.

We apply some of the techniques learned in the Techniques unit to solve problems involving number theory.

We apply some of the techniques learned in the Techniques unit to solve problems involving counting.

We apply some of the techniques learned in the Techniques unit to solve problems involving geometry.

In this final unit we present some concluding thoughts and solve a set of challenging problems that highlight most of the techniques and topics covered throughout the course.

© 2018 University of Waterloo. Except where noted, all rights reserved.

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Module 1: Problem Solving Strategies

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Unlike exercises, there is never a simple recipe for solving a problem. You can get better and better at solving problems, both by building up your background knowledge and by simply practicing. As you solve more problems (and learn how other people solved them), you learn strategies and techniques that can be useful. But no single strategy works every time.

Pólya’s How to Solve It

George Pólya was a great champion in the field of teaching effective problem solving skills. He was born in Hungary in 1887, received his Ph.D. at the University of Budapest, and was a professor at Stanford University (among other universities). He wrote many mathematical papers along with three books, most famously, “How to Solve it.” Pólya died at the age 98 in 1985.1

1. Image of Pólya by Thane Plambeck from Palo Alto, California (Flickr) [CC BY

In 1945, Pólya published the short book How to Solve It , which gave a four-step method for solving mathematical problems:

First, you have to understand the problem.

After understanding, then make a plan.

Carry out the plan.

Look back on your work. How could it be better?

This is all well and good, but how do you actually do these steps?!?! Steps 1. and 2. are particularly mysterious! How do you “make a plan?” That is where you need some tools in your toolbox, and some experience to draw upon.

Much has been written since 1945 to explain these steps in more detail, but the truth is that they are more art than science. This is where math becomes a creative endeavor (and where it becomes so much fun). We will articulate some useful problem solving strategies, but no such list will ever be complete. This is really just a start to help you on your way. The best way to become a skilled problem solver is to learn the background material well, and then to solve a lot of problems!

Problem Solving Strategy 1 (Guess and Test)

Make a guess and test to see if it satisfies the demands of the problem. If it doesn't, alter the guess appropriately and check again. Keep doing this until you find a solution.

Mr. Jones has a total of 25 chickens and cows on his farm. How many of each does he have if all together there are 76 feet?

Step 1: Understanding the problem

We are given in the problem that there are 25 chickens and cows.

All together there are 76 feet.

Chickens have 2 feet and cows have 4 feet.

We are trying to determine how many cows and how many chickens Mr. Jones has on his farm.

Step 2: Devise a plan

Going to use Guess and test along with making a tab

Many times the strategy below is used with guess and test.

Make a table and look for a pattern:

Procedure: Make a table reflecting the data in the problem. If done in an orderly way, such a table will often reveal patterns and relationships that suggest how the problem can be solved.

Step 3: Carry out the plan:

Notice we are going in the wrong direction! The total number of feet is decreasing!

Better! The total number of feet are increasing!

Step 4: Looking back:

Check: 12 + 13 = 25 heads

24 + 52 = 76 feet.

We have found the solution to this problem. I could use this strategy when there are a limited number of possible answers and when two items are the same but they have one characteristic that is different.

Videos to watch:

1. Click on this link to see an example of “Guess and Test”

http://www.mathstories.com/strategies.htm

2. Click on this link to see another example of Guess and Test.

http://www.mathinaction.org/problem-solving-strategies.html

Check in question 1:

Place the digits 8, 10, 11, 12, and 13 in the circles to make the sums across and vertically equal 31. (5 points)

Check in question 2:

Old McDonald has 250 chickens and goats in the barnyard. Altogether there are 760 feet . How many of each animal does he have? Make sure you use Polya’s 4 problem solving steps. (12 points)

Problem Solving Strategy 2 (Draw a Picture). Some problems are obviously about a geometric situation, and it is clear you want to draw a picture and mark down all of the given information before you try to solve it. But even for a problem that is not geometric thinking visually can help!

Videos to watch demonstrating how to use "Draw a Picture".

1. Click on this link to see an example of “Draw a Picture”

2. Click on this link to see another example of Draw a Picture.

Problem Solving Strategy 3 ( Using a variable to find the sum of a sequence.)

Gauss's strategy for sequences.

last term = fixed number ( n -1) + first term

The fix number is the the amount each term is increasing or decreasing by. "n" is the number of terms you have. You can use this formula to find the last term in the sequence or the number of terms you have in a sequence.

Ex: 2, 5, 8, ... Find the 200th term.

Last term = 3(200-1) +2

Last term is 599.

To find the sum of a sequence: sum = [(first term + last term) (number of terms)]/ 2

Sum = (2 + 599) (200) then divide by 2

Sum = 60,100

Check in question 3: (10 points)

Find the 320 th term of 7, 10, 13, 16 …

Then find the sum of the first 320 terms.

Problem Solving Strategy 4 (Working Backwards)

This is considered a strategy in many schools. If you are given an answer, and the steps that were taken to arrive at that answer, you should be able to determine the starting point.

Videos to watch demonstrating of “Working Backwards”

https://www.youtube.com/watch?v=5FFWTsMEeJw

Karen is thinking of a number. If you double it, and subtract 7, you obtain 11. What is Karen’s number?

1. We start with 11 and work backwards.

2. The opposite of subtraction is addition. We will add 7 to 11. We are now at 18.

3. The opposite of doubling something is dividing by 2. 18/2 = 9

4. This should be our answer. Looking back:

9 x 2 = 18 -7 = 11

5. We have the right answer.

Check in question 4:

Christina is thinking of a number.

If you multiply her number by 93, add 6, and divide by 3, you obtain 436. What is her number? Solve this problem by working backwards. (5 points)

Problem Solving Strategy 5 (Looking for a Pattern)

Definition: A sequence is a pattern involving an ordered arrangement of numbers.

We first need to find a pattern.

Ask yourself as you search for a pattern – are the numbers growing steadily larger? Steadily smaller? How is each number related?

Example 1: 1, 4, 7, 10, 13…

Find the next 2 numbers. The pattern is each number is increasing by 3. The next two numbers would be 16 and 19.

Example 2: 1, 4, 9, 16 … find the next 2 numbers. It looks like each successive number is increase by the next odd number. 1 + 3 = 4.

So the next number would be

25 + 11 = 36

Example 3: 10, 7, 4, 1, -2… find the next 2 numbers.

In this sequence, the numbers are decreasing by 3. So the next 2 numbers would be -2 -3 = -5

-5 – 3 = -8

Example 4: 1, 2, 4, 8 … find the next two numbers.

This example is a little bit harder. The numbers are increasing but not by a constant. Maybe a factor?

So each number is being multiplied by 2.

16 x 2 = 32

1. Click on this link to see an example of “Looking for a Pattern”

2. Click on this link to see another example of Looking for a Pattern.

Problem Solving Strategy 6 (Make a List)

Example 1 : Can perfect squares end in a 2 or a 3?

List all the squares of the numbers 1 to 20.

1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400.

Now look at the number in the ones digits. Notice they are 0, 1, 4, 5, 6, or 9. Notice none of the perfect squares end in 2, 3, 7, or 8. This list suggests that perfect squares cannot end in a 2, 3, 7 or 8.

How many different amounts of money can you have in your pocket if you have only three coins including only dimes and quarters?

Quarter’s dimes

0 3 30 cents

1 2 45 cents

2 1 60 cents

3 0 75 cents

Videos demonstrating "Make a List"

Check in question 5:

How many ways can you make change for 23 cents using only pennies, nickels, and dimes? (10 points)

Problem Solving Strategy 7 (Solve a Simpler Problem)

Geometric Sequences:

How would we find the nth term?

Solve a simpler problem:

1, 3, 9, 27.

1. To get from 1 to 3 what did we do?

2. To get from 3 to 9 what did we do?

Let’s set up a table:

Term Number what did we do

Looking back: How would you find the nth term?

Find the 10 th term of the above sequence.

Let L = the tenth term

Problem Solving Strategy 8 (Process of Elimination)

This strategy can be used when there is only one possible solution.

I’m thinking of a number.

The number is odd.

It is more than 1 but less than 100.

It is greater than 20.

It is less than 5 times 7.

The sum of the digits is 7.

It is evenly divisible by 5.

a. We know it is an odd number between 1 and 100.

b. It is greater than 20 but less than 35

21, 23, 25, 27, 29, 31, 33, 35. These are the possibilities.

c. The sum of the digits is 7

21 (2+1=3) No 23 (2+3 = 5) No 25 (2 + 5= 7) Yes Using the same process we see there are no other numbers that meet this criteria. Also we notice 25 is divisible by 5. By using the strategy elimination, we have found our answer.

Check in question 6: (8 points)

Jose is thinking of a number.

The number is not odd.

The sum of the digits is divisible by 2.

The number is a multiple of 11.

It is greater than 5 times 4.

It is a multiple of 6

It is less than 7 times 8 +23

What is the number?

Click on this link for a quick review of the problem solving strategies.

https://garyhall.org.uk/maths-problem-solving-strategies.html

MAE 5600 - Problem Solving as a Mathematical Endeavor (3)

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• Mathematical Problem Solving Course

Learn how to solve non-routine problems and think like a mathematician in either the fully online or face to face course for primary and high school teachers.

A 6-weeks fully online course was designed in partnership with Limina Education Services. Upon completing the intensive weekly course, teachers are tasked with completing a final assessment in the form of an online, randomised multiple-choice test designed to assess the knowledge and skills they acquired during the course.

The multiple-choice questions are carefully selected and graded from easy to hard to ensure that they provide an accurate measure of each teacher’s understanding of core concepts and ability to apply them in real-world scenarios.

The course has been developed by Alwyn Olivier and Dr Erna Lampen. It is a self-paced fully online course. Teachers must commit to work 2-3 hours per week on the course and attend weekly live sessions.

Course units:

Unit 1: What is a Problem?

Unit 2: Control the Problem-Solving Process

Unit 3: Focus on Structure

Unit 4: The Power and Pitfalls of Induction

Unit 5: Think like a Mathematician - Structure,             Control, Generalise, Pose New Problems

Unit 6: Think Like a Mathematician - be systematic.

The face to face courses are normally presented on two Saturdays and focus on the improvement of mathematical problem solving skills. It consists of the following levels:

Primary (grades 4 - 7).

Learning about problem solving (strategies, specialisation and generalisation, induction and deduction). Medium through which the course is presented is through problem solving, i.e. teachers learn to solve problems by problem solving.  The end objective is that teachers will enter and prepare their learners for the South African Mathematics Challenge.

GET Level 1

Introduction to problem solving strategies; offered to all teachers who are doing the course for the first time. The course comprises of the Junior First Round questions of the South African Mathematics Olympiad and involves a range of problem solving strategies.

GET Level 2

Offered to all teachers who have passed GET Level 1 or FET Level 1.  The course comprises of the Junior Second Round questions of the South African Mathematics Olympiad and involves a range of problem solving strategies.

GET Level 3

Offered to all teachers who have passed GET Level 1, GET Level 2 or FET Level 1. The course comprises of the Junior Third Round questions of the South African Mathematics Olympiad and involves a range of advanced problem solving strategies including producing a convincing proof or argument to substantiate a certain conclusion.

FET Level 1

Offered to all teachers who have passed GET Level 1.  The course comprises of the Senior First Round questions of the South African Mathematics Olympiad and involves a range of problem solving strategies.

Assessment & Certification:

Assessment will take on the form of a test which will inform the process of awarding Certificates of Achievement.

The teachers will be awarded certificates as follows:

• 50% and above but less than 75% will receive a pass certificate.
• 75% and above will receive a merit certificate.

All levels are endorsed by the South African Council of Educators and can be used for continuous professional development (CPD points are awarded per level).

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Marking a Milestone: Four Years of Daily Study Groups

From data to discovery: studying computational biology with wolfram, navigating quantum computing: accelerating next-generation innovation, unlock innovative problem-solving skills with creative computation.

As computers continue to perform an increasing number of tasks for us, it’s never been more important to learn how to use computers in creative ways. Creative computing, an interdisciplinary subject combining coding with artistic expression, allows us to blend technology with human experiences. Learning to create in this way can help you unlock your innovative problem-solving skills. By mastering creative computation, you can create interactive artwork, design immersive experiences and develop creative solutions to real-world challenges.

Wolfram U ’s new Creative Computation course combines an introduction to Wolfram Language coding with a project-based exploration of various art forms, like visual art, poetry, audio and video game design. If you’ve never coded in Wolfram Language before, this course is a fantastic introduction to applied computing and will help you learn the language for any project. If you’ve already mastered the basics of coding, this course will help you apply your skills to fascinating new problems and projects.

We would love for you to join us in this interactive course as we explore what it means to work creatively with coding.

Motivation from History

Creative computing is a relatively new subject, but people have been using technology to make art for centuries. From the loom to the printing press or Walkman to Atari, technology has been part of art for as long as both have existed.

We now have a variety of exciting and creative ways to engage with computers, from AI-generated images to immersive virtual realities.

In this course, you will learn how to use Wolfram Language to create various forms of art. There are four main sections to the course: Computational Art, Computational Strings, Sound and Game Development. In each section, there are lessons teaching Wolfram Language skills, with associated exercises, and at the end of each section, there is a larger project. The projects are designed for you to stretch your creative muscles and use your new coding skills to create art. You’ll learn how to create visual art using images, how to write poetry using string manipulation, how to visualize audio and how to make text-based and graphics-based video games, all while learning how to code in Wolfram Language.

Here is a sneak peek at some of the topics in the course (shown in the left-hand column):

With 16 lessons, five quizzes and four projects, this course should take around five hours to complete. We recommend doing all the activities and projects to maximize your understanding and explore your new skills.

There is no background required to participate in this course. We will teach you all the coding skills you need to make the projects, so all that is required is your excitement and creativity.

Let’s explore what’s in the course.

There are 16 lessons in this course spread out over the five total sections (Computational Thinking and Coding, Computational Art, Computational Strings, Sound and Game Development). In each lesson, you will explore a different aspect of coding through a short video. You’ll start off by exploring the concept of computational thinking: how to translate your thoughts and your creativity into something the computer can understand and how to work with a computer to build creative artifacts. Here is a short excerpt from the video for this lesson:

Each lesson teaches a specific coding skill, with lots of examples and exploration of key concepts. In the Computational Art section, the goal is to use images and graphics to create a piece of art. In order to do that, we need to learn skills like variables, functions, lists, the Table and Map functions, colors, graphics and randomness, and image manipulation. Each skill is taught with an interactive video lesson in conjunction with exercises, before you use the project to test your knowledge.

The video lessons range from 5–13 minutes in length, and each video is accompanied by a transcript notebook displayed on the right-hand side of the screen. You can copy and paste Wolfram Language input directly from the transcript notebook to the embedded scratch notebook to try the examples for yourself.

Each lesson has a set of exercises to review the concepts covered during the lesson. Since this course is designed for independent study, a detailed solution is given for all exercises. Each exercise will help you practice a specific skill you’ve learned so that you are ready to use that skill in the project. Here is an example of an exercise from lesson 6 on image manipulation:

The exercise notebooks are interactive, so you can try variations of each problem in the Wolfram Cloud . You’re encouraged to blend skills together as you learn them. For example, for the aforementioned exercise, you could use the skills you just learned about randomness to replace the dominant colors in the image of the wolf with random colors, or you could import images to do the same exercise with a different image. When you’ve gotten further in the course, you could come back and build your own function that can do this to any two images.

Each section of the course includes a short project, and the Game Development section has two longer projects. In each case, you’ll use the skills you learned in that section to build something creative. In the first three sections, we provide detailed solutions and walk you though our processes, but in the Game Development section, we encourage you to build something unique.

In the Computational Art section, you’ll make art using images and shapes. In Computational Strings, you’ll write a Mad Libs haiku. In Sound, you’ll make an audio visualizer. In Game Development, you’ll make a text adventure game and a graphics-based Pac-Man –style game.

These projects will allow you to celebrate your successes and practice your new coding skills while cementing your understanding of creative computation.

Each section of the course ends with a short quiz, which allows you to demonstrate your understanding:

You will get instant feedback on your solutions, and you’re encouraged to try out the code.

Course Certificate

You are encouraged to watch all the lessons and attempt the projects and quizzes in the recommended sequence, since each topic in the course relies on earlier concepts and techniques. When you watch all 16 lesson videos and pass the five course quizzes, you will earn a certificate of course completion. The Track My Progress status bar in the course helps you to chart your progress, showing you where you left off from your previous course session. While you don’t have to submit projects to earn a certificate, they are a fundamental part of gaining computational skills, and we look forward to connecting with course users about their projects on Wolfram Community . Your course certificate represents completion of the basic course requirements, demonstrates your interest in exploring the latest technology and in building new computational skills, and it will add value to your resume or social media profile.

You are also encouraged to use the skills you learn in this course to go on to earn Level 1 certification for Wolfram Language proficiency . While the course does not require the same level of mathematics as the Level 1 certification exam, it will prepare you well for accomplishing the range of computational tasks that are required for Level 1 certification.

A Building Block for Success

A mastery of the fundamental concepts of creative computing will prepare you for working with computers to innovatively solve problems. Whether you’re interested in creating art or you’re interested in developing your coding skills, this course will provide a detailed foundation in both. Learning Wolfram Language is a valuable pursuit regardless of your career aspirations, as you can use the skills you learn in this course in any field.

Acknowledgements

I would like to thank my coauthor Eryn Gillam for their major contributions to the development of this course, as well as others who helped this course come together, including (but not limited to) Anisha Basil, Abrita Chakravarty, Cassidy Hinkle, Joyce Tracewell, Arben Kalziqi, Isabel Skidmore, Zach Shelton, Simeon Buttery, Ryan Domier and Eder Ordonez.

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