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Geometry and the Mathematics of Design

MATH 1536 is offered in the Spring semester only.

A standard first-year mathematics sequence for architecture majors. Mathematical models of real-world problems, including discrete and continuous models, that address relevant global challenges in such areas as urban planning, building construction, and home design. Vectors in the plane and space, descriptive and projective geometry, differential and integral calculus, applications for 2- and 3-dimensional design and construction, including areas, volumes, centroids, and optimization. (3H,3C)

Prerequistes: 2 units of high school algebra and 1 unit of high school geometry.

Required Online Textbook: Geometry and Mathematics of Design

Chapter   Section   Subject
1.1    Vectors in the Plane
  1.1.1 Geometric and Algebraic Vectors
  1.1.2 Addition, Subtraction, and Scalar Multiplication
  1.1.3 Magnitude and Unit Vector
1.2   Vectors in Space
  1.2.1 Vectors and Operations
  1.2.2 Vectors and Unit Cube
1.3   Dot Product
  1.3.1 Dot Product Definition
  1.3.2 Angle Between Two Vectors
  1.3.3 Orthogonal Vectors
1.4   Cross Product
  1.4.1 Cross Product Definition
  1.4.2 Parallel and Coplanar Vectors
  1.4.3 Areas and Volumes
  1.4.4 Special Area Rules
1.5    Planes
  1.5.1 Normal Vector
  1.5.2 Equation of a Plane
  1.5.3 Angle Between Planes
  1.5.4 Distance Between Parallel Planes
1.6   Lines in Space
  1.6.1 Equations of a Line in Space
  1.6.2 Intersection of Lines and Planes
Chapter  Section  Topic
2.1    Descriptive Geometry
  2.1.1  Orthogonal Projections
  2.1.2  Projecting Onto 2-D View Planes
  2.1.3  Constructing 3-D Objects from View Planes
  2.1.4  Projecting Polygons and Intersecting Lines
  2.1.5  Projecting Lines Intersecting Polygons
2.2    Projective Geometry in 2-D
  2.2.1  Introduction
  2.2.2  Cross Ratios
  2.2.3  Complete Quadrilaterals
2.3   Projective Geometry in 3-D
  2.3.1  One Point Perspective
  2.3.2  Two Point Perspective
  2.3.3  Three Point Perspective
Chapter Section Topic
3.1   Functions and Tangent Lines
  3.1.1 Function Basics
  3.1.2 Tangent Lines
  3.1.3 Limiting Process
3.2   Derivatives
  3.2.1 Derivative Definition
  3.2.2 Basic Derivative Rules
  3.2.3 Chain Rule
  3.2.4 Constant Multiple and Sum Rules
  3.2.5 Product Rule
3.3   Derivative Applications
  3.3.1 Solving Problems with Derivatives
  3.3.2 Local Extrema
  3.3.3 Optimization
Chapter Section Topic
4.1   Approximating Areas
  4.1.1 Approximate Areas Visually
  4.1.2 Polygon and Circle Areas
  4.1.3 Riemann Sums
4.2   Integrals
  4.2.1 Antiderivatives
  4.2.2 Definite Integral
  4.2.3 Definite Integral Properties
  4.2.4 Evaluate Definite Integrals
  4.2.5 Substitution
4.3   Areas
  4.3.1 Area Between f(x) and the X-axis
  4.3.2 Area Between Two Curves
4.4   Centroids
  4.4.1 Finite Masses Concentrated at a Point
  4.4.2 Triangles and Rectangles
  4.4.3 Thin Flat Plates
4.5   Volumes
  4.5.1 Prisms and Pyramids
  4.5.2 Disk/Washer Method
  4.5.3 Cylindrical Shell Method

Check your instructor's Canvas course site for the date and time of your final exam.

During any Spring Semester, see the Timetable of classes for information on current offerings of MATH 1536.


  • The in-person version of MATH 1536 consists of two 75 minute lectures. 
  • All quizzes can be taken at home and are unproctored.
  • The midterm exams and the final exam are  taken in the testing center at the Math Emporium. The quizzes and exams are multiple choice.

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“As a Hokie, I will conduct myself with honor and integrity at all times. I will not lie, cheat, or steal, nor will I accept the actions of those who do.”

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If you are currently enrolled in MATH 1536, you can contact your instructor through your Canvas course website.