About the Course
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
Learning Objectives
- Define and distinguish between inductive, deductive, and abductive reasoning, providing examples of each
- Explore and explain the relationship between number patterns and geometry, using both explicit and recursive formulas
- Translate logic statements and defend premises by using symbolic logic connectives and constructing and interpreting truth tables
- Apply the principles of logic to identify the premises and conclusions of various types of arguments, and defend conclusions or assess the validity of those arguments
- Solve problems using algebraic, geometric, and symbolic representations using manipulatives or models
- Share and articulate ideas and solutions to problems, both written and orally, independently and in groups
About Advanced Enrichment courses
These courses offer above-grade-level material that is presented in a novel context, explored with other advanced learners, and guided by a CTY educator to help prepare students for higher-order thinking and college-style academic challenges. Students work individually and may finish the course early if they complete all requirements before the course end date.
Requirements
CTY courses have grade-level requirements and most require minimum test scores. Some courses may also have prerequisites.
Identification DetailsDates and Tuition
In Person
Speyer School
New York, NY
Day Site
You will be asked to join or sign in first.
Register by: June 21, 2026
Full Waitlist Available
Time Commitment:
Course Materials
Students should bring basic school supplies like pens, notebooks, and folders to their summer program. You will be notified of any additional items needed before the course begins. All other materials will be provided by CTY.
Sample Reading
These titles have been featured in past sessions of the course, and may be included this summer. CTY provides students with all texts; no purchase is required.
The Number Devil, by Hans Magnus Enzensberger
You will be asked to join or sign in first.
Register by: July 12, 2026
Full Waitlist Available
Time Commitment:
Course Materials
Students should bring basic school supplies like pens, notebooks, and folders to their summer program. You will be notified of any additional items needed before the course begins. All other materials will be provided by CTY.
Sample Reading
These titles have been featured in past sessions of the course, and may be included this summer. CTY provides students with all texts; no purchase is required.
The Number Devil, by Hans Magnus Enzensberger
UC-Santa Cruz
Santa Cruz, CA
Residential Site
You will be asked to join or sign in first.
Register by: June 21, 2026
Time Commitment:
Course Materials
Students should bring basic school supplies like pens, notebooks, and folders to their summer program. You will be notified of any additional items needed before the course begins. All other materials will be provided by CTY.
Sample Reading
These titles have been featured in past sessions of the course, and may be included this summer. CTY provides students with all texts; no purchase is required.
The Number Devil, by Hans Magnus Enzensberger
You will be asked to join or sign in first.
Register by: July 12, 2026
Time Commitment:
Course Materials
Students should bring basic school supplies like pens, notebooks, and folders to their summer program. You will be notified of any additional items needed before the course begins. All other materials will be provided by CTY.
Sample Reading
These titles have been featured in past sessions of the course, and may be included this summer. CTY provides students with all texts; no purchase is required.
The Number Devil, by Hans Magnus Enzensberger
Registration Fee and Financial Aid
Tuition and fees will be waived or reduced for students who qualify for financial aid.
Learn more about Financial Aid