When was mathematical thinking born? What knowledge did architects have 4 thousand years ago? How were the pyramids built? What is the “golden” ratio? Are there perfect numbers? Where is Math hiding in the Parthenon? Why is the seating area in ancient Greek theaters in a circular shape?

In this course, we will analyze the use of Mathematics in Architecture over the centuries and its use by different cultures. Starting from the beginning of counting and geometry, we will discover how the ancient architects used their mathematical knowledge in each period. We will travel to Ancient Egypt, learn about the cultural development of the Sumerians and the Babylonians of Mesopotamia and discover the great contribution of Greek mathematics in Ancient Greece.

Students will have the opportunity to learn about monumental construction achievements of the ancient civilizations and the application of mathematics in them, to find hidden “golden” numbers, to create their own constructions and to discover how mathematics are manifested in the impressive constructions of the Egyptians, the Mesopotamians and the Ancient Greeks.

You meet a new friend at CTY who teaches you a dice game. The rules are simple: if you roll a 4, you win and the game ends. If your friend rolls a 5, she wins and the game ends. You take turns rolling until one person wins. If you roll first, what is the probability that you will win the game? There are several ways to solve this problem, and the answer is not obvious.

In this course, students develop a greater understanding of probability and statistics, two areas of mathematics that easily transfer from the classroom to the real world. Students conduct experiments and generate data which they display in graphs, charts, and tables in order to compare the effects of particular variables. For example, students might analyze data to examine how various design characteristics of a paper airplane, such as weight or length, affect the distance it will travel. In addition, students consider other data sources, including newspapers and journals, and identify examples of incorrectly gathered or misrepresented data that have been used to mislead consumers or influence voters.

Students also explore probability, the study of chance, to learn how to use numerical data to predict future events. Students examine permutations and combinations; develop strategies for calculating the number of possible outcomes for various events; calculate probabilities of independent, dependent, and compound events; and learn to distinguish between theoretical and experimental probability.

Did you know that if one person’s DNA was unraveled and placed end to end, it would stretch to the sun and back at least 60 times? Or that humans and chimps share a surprising 98.8 percent of their DNA? How can we be so similar and yet so different? How does all that relate to having your mother’s eyes, or your father’s nose? Or even your great grandmother’s hair? And how did complex, multicellular organisms evolve from simpler, single-celled ones? We begin with an exploration of Mendelian genetics to determine how simple traits are passed from parents to offspring, delve into more complex concepts such as sex-linked traits and polygenic inheritance, to move towards understanding the genetics of inherited disorders. We will also take a look into the fascinating world of 6 million years of evolution. Furthermore, we learn and practice some of the methods and techniques that geneticists use to explore these concepts, such as PCR, gel electrophoresis, and bacterial transformations. 

Learning objectives

• Predict the impact of mutations and the inheritance patterns of different diseases.
• Utilize biotechnological laboratory skills to determine the genotypes of individuals and explore the process of transformation, a key technique in genetic engineering. 
• Research and present a genetically inherited disease/syndrome including characteristics such as genetic heterogeneity, penetrance and expressivity.