Week four logic: STATEMENTS

Logic is a systematic way of thinking that allows us to parse the meanings of sentences and to deduce new information from old information. In this session, we learned what is a statement, how to use a truth table, and different ways of combining statements. Using these building blocks, we solved puzzles on truth tables, logic language, and implications.

Week FIVE LET’S HAVE SOME FUN: werewolves (loups-garous)

From previous sessions, we learned to distinguish logical structures and understand the meanings of logical statements. We also learned useful tools to organize information and understand statements. Sometimes it is necessary or helpful to parse them into expressions involving logic symbols. This may be done mentally or on scratch paper, and the thinking process can be expressed verbally or illustrated by a diagram. In this session, we will play Werewolves, a game involves strategical thinking and logical deduction. which will give you sufficient practice in translating English sentences into logical statements and interpreting clues in logical manner.

wEEK six LOGICAL equivalences

In general, two statements are logically equivalent if their truth values match up line-for-line in a truth table. Logical equivalence is important because it can give us different (and potentially useful) ways of looking at the same thing. There are some significant logical equivalences such as contrapositive law, DeMorgan’s Law, commutatives laws, distributive laws, and assosiative laws.

In this session, we went over logical equivalences and apply them to solve logical problems.

Bank of Puzzles

WEEK SEVEN COUNTING PRINCIPLES

Combinatorics is the study of counting. It develops techniques to count outcomes, arrangements, and combinations of objects. These counting strategies can be applied to various disciplines such as pure mathematics, quantum computation, biochemistry, and computer science.

Some combinatorics problems arise from situations that appear chaotic at first. Hence it is important to focus on ways to organize objects being counted. For example, look for ways to “simplify” the number of objects being counted: separate them into cases, focus only on the ones that meet certain criteria, and look for patterns.

This week, we will talk about counting principles such as the multiplication principle, the addition principle, the subtraction principle, and the inclusion-exclusiom principle. We will use some examples to demonstrate how to apply these principles to solve a problem.

WEEK EIGHT & NINE PERMUTATION AND COMBINATION

Without replacement, there are various ways to select objects from a set to form subsets, such as permutation and combination. Permutation is applied when we account for the order of selection, while combination is used when order doesn’t matter.

In real life, we used permutation and combination to arrange objects and study patterns. In science, these principles are used widely in areas such as communication networks, databases and data mining, computer architecture, computational molecular biology, linguistics, etc.

This week, we will learn about these two principles and use them to solve counting problems.

WEEK TEN & ELEVEN cOMBINATORICS CARNIVAL

In the past two weeks, we learned counting principles such as addition principles, multiplication principles, subtraction principles, and inclusion-exclusion principles. We also learned to apply permutation and combination in different scenarios.

This week, we will use these counting techniques to solve various combinatorics problems.

week twelve LOGIC & DISCRETE MATHEMATICS IN THE REAL WORLD

Mathematics is useful in solving a very wide variety of practical problems. This term we focused on discrete mathematics, which underpins about half of the pure mathematics and contributes to a wide range of research activities. But what are some actual applications where discrete mathematics can be applied? What problems are being solved?

This week, we will describe interesting problems arised from all walks of life, and see how logic and discrete mathematics are used to solve these problems.