Algebra

• Arithmetic sequences and series; sum of finite arithmetic series; geometric sequences and series; sum of finite and infinite geometric series.
• Sigma notation.
• Applications.

• Technology may be used to generate and display sequences in several ways.
• Link to 2.6, exponential functions.
• Examples include compound interest and population growth.

• Int: The chess legend (Sissa ibn Dahir).
• Int: Aryabhatta is sometimes considered the “father of algebra”. Compare with al-Khawarizmi.
• TOK: How did Gauss add up integers from 1 to 100? Discuss the idea of mathematical intuition as the basis for formal proof.
• TOK: Debate over the validity of the notion of “infinity”: finitists such as L. Kronecker consider that “a mathematical object does not exist unless it can be constructed from natural numbers in a finite number of steps”.
• TOK: What is Zeno’s dichotomy paradox? How far can mathematical facts be from intuition?

• Elementary treatment of exponents and logarithms.
• Laws of exponents; laws of logarithms.
• Change of base.

• Appl: Chemistry 18.1 (Calculation of pH ).
• TOK: Are logarithms an invention or discovery? (This topic is an opportunity for teachers to generate reflection on “the nature of mathematics”.)

• The binomial theorem:
• expansion of (a + b), n∈N .
• Calculation of binomial coefficients using Pascal’s triangle and
• 

Not required:

• formal treatment of permutations and formula for ⁿP_r.

• Counting principles may be used in the development of the theorem.
• should be found using both the formula and technology.
• Example: finding  from inputting y = 6ⁿ C_r X and then reading coefficients from r the table.
• Link to 5.8, binomial distribution.

• Aim 8: Pascal’s triangle. Attributing the origin of a mathematical discovery to the wrong mathematician.
• Int: The so-called “Pascal’s triangle” was known in China much earlier than Pascal.