About the Course

Inductive and Deductive Reasoning

  • Grades 5-6
  • CTY-Level
  • Residential and Commuter
  • Mathematics

Reasoning, logic, and critical thinking are the building blocks of intellectual inquiry. This course will help develop your skills in these areas through problem-solving and exposure to a wide range of topics in mathematics. You’ll learn the different techniques used in inductive and deductive reasoning and examine the roles each play in the field of mathematics. First you’ll explore algebraic and geometric concepts, patterns, and real-world questions that can be answered using inductive reasoning, creating recursive and explicit formulas to describe patterns. As you move on to deductive reasoning, you’ll learn to use a system of logic to draw conclusions from statements that are accepted as true. Explore fun approaches to this style of reasoning, such as symbolic logic, truth tables, and syllogisms, while learning how to construct valid arguments to reach conclusions.

Typical Class Size: 14-16
 

Course Overview

This course is

ungraded.

Summer Dates & Locations

Registration deadline:

After May 9, 2025, registration is available upon request pending eligibility and seat availability. To request placement, email [email protected] after submitting a program application.

Session One

Image of Roger Williams University
Bristol, Rhode Island
-
Residential cost: $7,259
Commuter cost: $6,459
image of the Loyola Marymount University campus
Los Angeles, California
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Residential cost: $7,501
Commuter cost: $6,701
Image of the University of California Santa Cruz campus
Santa Cruz, California
-
Residential cost: $7,501
Commuter cost: $6,701
Image of Speyer School in New York City
New York, New York
-
Day cost: $3,959

Session Two

Image of Roger Williams University
Bristol, Rhode Island
-
Residential cost: $7,259
Commuter cost: $6,459
image of the Loyola Marymount University campus
Los Angeles, California
-
Residential cost: $7,501
Commuter cost: $6,701
Birdseye view image of the campus of Mirman School
Los Angeles, California
-
Day cost: $3,959
Image of the University of California Santa Cruz campus
Santa Cruz, California
-
Residential cost: $7,501
Commuter cost: $6,701
Image of Speyer School in New York City
New York, New York
-
Day cost: $3,959

Testing and Prerequisites

  Math Verbal
Required Level CTY-Level Not required
Check your eligibility using existing test scores If you do not have existing test scores:

Students must achieve qualifying scores on an advanced assessment to be eligible for CTY programs. If you don’t have qualifying scores, you have several different testing options. We’ll help you find the right option for your situation.

Sign up for Testing Learn More

Cost and Financial Aid

  • Tuition
    • Varies
  • Application fee
    • Nonrefundable Application Fee - $55 (Waived for financial aid applicants)
    • Nonrefundable International Fee - $250 (outside US only)

Financial Aid is available
We are committed to serving all talented youth regardless of financial circumstances. Financial assistance is available based on need.

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About Mathematics at CTY

Explore the study of shapes

Many of our courses allow students to describe the world around them in basic and profound ways. Younger students build foundational skills by exploring shape, scale, and proportion in Geometry and Spatial Sense. Middle School students delve into real-world applications of lines and analyze data with curves that follow uniform, symmetric, bell-shaped, or skewed patterns in Data and Chance. Advanced students unveil the deep interplay between numbers and shapes, investigating how triangular, square, and polygonal numbers create patterns that bridge geometry and algebra in Number Theory. By examining these elegant number patterns and symmetries, students discover how mathematics captures the intricate beauty and underlying structure of the natural world.

Dive deep into logic and reasoning

Our courses in formal logic give you the tools to question the world around you. Inductive and Deductive Reasoning introduces younger students to different types of reasoning, as well as the strengths and weaknesses inherent in various forms of critical analysis. Older students explore how logical reasoning can explain (or fail to explain) counter-intuitive results in Paradoxes and Infinities, or take a more rigorous approach to formal logic in Mathematical Logic.

Meet our instructors and staff