Mathematics for Game Developers

Students interested and engaged in game development careers are often underprepared for direct entry into a Calculus sequence. Students who are hesitant to study computer science are often interested and engaged in gaming. That’s what led to this set of activities; cloaking advanced mathematics to build confidence for teachers and students on a set of topics intimidating for educators and overwhelming for students.

We view this offering as a series of activities rather than a math book. Each activity includes short descriptions and examples, and most have teacher notes at the end of the activity. Feel free to edit to support your students.

We made every effort for all documents to pass all accessibility screenings. Graphs and math equations are complex by their nature. We have created .pdf versions with ALT text for all images and .docx versions that work with all JAWS screen readers. If you have an interest in advising, please get in touch with KellyCooper@OER4CTE.org

The Unit title, in the Table of Contents toward the bottom of this page, links to both accessible .pdf and .docx files of each Unit of the Student Edition.

To receive the Teacher’s Edition files, please email KellyCooper@LivableWageJobs.org

The digital versions of the book are free. We hope to hear from you regarding how the materials can be improved or added to. Everything is CCby4 – free to use, edit, and adapt with attribution. Please attribute to Downey Unified School District and MathForGameDevelopers.com

To order a printed book:

Lulu Press link to a Student’s Edition printed book for $9.14 plus tax and shipping

DOWNEY UNIFIED SCHOOL DISTRICT, PUBLISHER

Links below lead to .pdf and .docx files of each Student Edition unit.

UNIT 1 SOME BASIC ALGEBRA (.pdf of Unit 1)
UNIT 1 SOME BASIC ALGEBRA SCREEN READER VERSION (.docx of Unit 1)
1.1 CONSTANTS, VARIABLES, AND EXPRESSIONS
• A BIT MORE DETAIL
• MATHEMATICAL EXPRESSIONS
• USING TECHNOLOGY
• EXAMPLES

UNIT 2 VECTORS IN TWO DIMENSIONS (.pdf of Unit 2)
UNIT 2 VECTORS IN TWO DIMENSIONS SCREEN READER VERSION (.docx of Unit 2)
2.1 VECTORS
• VECTORS IN STANDARD POSITION
• COMPONENTS OF A VECTOR
• ROW AND COLUMN FORMS OF A VECTOR
• EQUAL VECTORS
• EXAMPLES

2.2 ADDITION, SUBTRACTION, AND SCALAR MULTIPLICATION OF VECTORS
• ADDITION and SUBTRACTION OF VECTORS
• SCALARS
• USING TECHNOLOGY
• EXAMPLES

2.3 MAGNITUDE, DIRECTION, AND COMPONENTS OF A VECTOR
• THE MAGNITUDE OF A VECTOR
• THE DIRECTION OF A VECTOR
• THE COMPONENTS OF A VECTOR
• USING TECHNOLOGY
• EXAMPLES

2.4 THE DOT PRODUCT OF TWO VECTORS, THE LENGTH OF A VECTOR, AND THE ANGLE BETWEEN TWO VECTORS
• THE DOT PRODUCT OF TWO VECTORS
• THE LENGTH OF A VECTOR
• THE ANGLE BETWEEN TWO VECTORS
• USING TECHNOLOGY
• EXAMPLES

2.5 PARALLEL AND PERPENDICULAR VECTORS, THE UNIT VECTOR
• PARALLEL AND ORTHOGINAL VECTORS
• THE UNIT VECTOR
• USING TECHNOLOGY
• EXAMPLES

2.6 THE VECTOR PROJECTION OF ONE VECTOR ONTO ANOTHER
• PROJECTION
• USING TECHNOLOGY
• EXAMPLES

UNIT 3 VECTORS IN THREE DIMENSIONS (.pdf of Unit 3)
UNIT 3 VECTORS IN THREE DIMENSIONS SCREEN READER VERSION (.docx of Unit 3)
3.1 THREE DIMENSIONAL VECTORS
• 3-DIMENSIONAL SPACE
• THE DISTANCE BETWEEN TWO POINTS IN 2 AND 3-DIMENSIONAL SPACE
• USING TECHNOLOGY
• THE EQUATION OF A CIRCLE AND A SPHERE
• EXAMPLES

3.2 MAGNITUDE AND DIRECTION COSINES OF A VECTOR
• THE MAGNITUDE OF A VECTOR
• THE DIRECTION COSINES OF VECTORS IN 2- AND 3-DIMENSIONS
• USING TECHNOLOGY
• EXAMPLES

3.3 ARITHMETIC ON VECTORS IN 3-DIMENSIONAL SPACE
• ADDITION AND SUBTRACTION OF VECTORS
• SCALAR MULTIPLICATION
• USING TECHNOLOGY
• EXAMPLES

3.4 THE UNIT VECTOR IN 3-DIMENSIONS AND VECTORS IN STANDARD POSITION
• THE UNIT VECTOR IN 3-DIMENSIONS
• VECTORS IN STANDARD POSITION
• NORMALIZING A VECTOR
• EXAMPLES
• USING TECHNOLOGY

3.5 THE DOT PRODUCT, LENGTH OF A VECTOR, AND THE ANGLE BETWEEN TWO VECTORS IN THREE DIMENSIONS
• THE DOT PRODUCT OF TWO VECTORS
• THE LENGTH OF A VECTOR IN THREE DIMENSIONS
• THE ANGLE BETWEEN TWO VECTORS
• USING TECHNOLOGY
• EXAMPLES

3.6 THE CROSS PRODUCT: ALGEBRA
• THE CROSS PRODUCT OF TWO VECTORS
• USING TECHNOLOGY
• THE RIGHT-HAND RULE
• USING TECHNOLOGY
• EXAMPLES

3.7 THE CROSS PRODUCT: GEOMETRY
• THE CROSS PRODUCT OF TWO VECTORS AND THE RIGHT-HAND RULE
• THE GEOMETRY OF THE CROSS PRODUCT
• USING TECHNOLOGY
• AREA OF A PARALLELOGRAM
• THE CROSS PRODUCT OF PERPENDICULAR AND PARALLEL VECTORS
• EXAMPLES

UNIT 4 MATRICES (.pdf of Unit 4)
UNIT4 MATRICES SCREEN READER VERSION (.docx of Unit 4)
4.1 MATRICES
• MATRIX
• DIMENSION OF A MATRIX
• ELEMENTS OF A MATRIX
• EQUAL MATRICES
• SQUARE MATRICES
• MAIN DIAGONAL OF A SQUARE MATRIX
• THE IDENTITY MATRIX
• THE ZERO MATRIX
• THE TRANSPOSE OF A MATRIX
• ROW MATRICES AND COLUMN MATRICES
• VECTORS AS MATRICES
• EXAMPLES

4.2 ADDITION, SUBTRACTION, SCALAR MULTIPLICATION, AND PRODUCTS OF ROW AND COLUMN MATRICES
• ADDITION AND SUBTRACTION OF MATRICES
• EXAMPLE
• SCALAR MULTIPLICATION
• EXAMPLE
• MULTIPLICATION WITH ROW AND COLUMN MATRICES
• EXAMPLE
• MOTIVATION FOR THE PROCESS OF MULTIPLICATION WITH ROW AND COLUMN MATRICES
• IMPORTANT OBSERVATION-SEE THIS
• DIMENSION MATTERS
• EXAMPLES

4.3 MATRIX MULTIPLICATION
• COMPATIBLE MATRICES
• MATRICES AS COLLECTION OF ROW AND COLUMN MATRICES
• MULTIPLICATION OF TWO MATRICES
• EXAMPLE
• USING TECHNOLOGY
• EXAMPLES

4.4 ROTATION MATRICES IN 2-DIMENSIONS
• THE ROTATION MATRIX
• THE ROTATION PROCESS
• USING TECHNOLOGY
• EXAMPLES

4.5 FINDING THE ANGLE OF ROTATION BETWEEN TWO ROTATED VECTORS IN 2-DIMENSIONS
• GIVEN THE ROTATED VECTOR, FIND THE ANGLE OF ROTATION
• USING TECHNOLOGY
• EXAMPLES

4.6 ROTATION MATRICES IN 3-DIMENSIONS
• THE THREE BASIC ROTATIONS
• THE ROTATION MATRICES
• THE ROTATION PROCESS
• THE X-AXIS
• THE Y-AXIS
• THE Z-AXIS
• USING TECHNOLOGY
• EXAMPLES

UNIT 5 SOME BASIC TRIGONOMETRY (.pdf of Unit 5)
UNIT 5 SOME BASIC TRIGONOMETRY SCREEN READER VERSION (.DOCX of Unit 5)
5.1 THE BASIC TRIGONOMETRIC FUNCTIONS
• RIGHT TRIANGLE TRIGONOMETRY
• THE SINE OF AN ANGLE
• THE COSINE OF AN ANGLE
• THE TANGENT OF AN ANGLE
• USING TECHNOLOGY
• EXAMPLES

5.2 CIRCULAR TRIGONOMETRY
• THE SINE FUNCTION OF THE UNIT CIRCLE
• THE COSINE FUNCTION ON THE UNIT CIRCLE
• THE SINE AND COSINE FUNCTION ON ANY CIRCLE
• EXAMPLES

5.3 GRAPHS OF THE SINE FUNCTION
• DISCRETE GRAPH OF THE SINE FUNCTION FROM 0° TO 90°
• GRAPHS OF THE HEIGHTS
• THE CONTINUOUS SINE CURVE FROM 0° TO 90°
• THE CONTINUOUS SINE CURVE FROM 0° TO 180°
• THE CONTINUOUS SINE CURVE FROM 0° TO 360°
• THE EXTENDED SINE CURVE
• EXAMPLES

5.4 GRAPHS OF THE COSINE FUNCTION
• DISCRETE GRAPH OF THE COSINE FUNCTION FROM 0° TO 360°
• THE EXTENDED COSINE CURVE
• EXAMPLES

5.5 AMPLITUDE AND PERIOD OF THE SINE AND COSINE FUNCTIONS
• AMPLITUDE
• THE AMPLITUDE OF Y = ASIN0 AND Y = ACOS0
• PERIOD
• THE PERIOD OF Y = SINB0 AND Y = COSB0
• USING TECHNOLOGY
• EXAMPLES