Mathematics **analysis and approaches** are for students who enjoy developing their mathematics to become fluent in the construction of mathematical arguments and develop strong skills in mathematical thinking. They will also be fascinated by exploring real and abstract applications of these ideas, with and without technology. Students who take Mathematics: analysis and approaches will be those who enjoy the thrill of mathematical problem solving and generalization.

This course recognizes the need for analytical expertise in a world where innovation is increasingly dependent on a deep understanding of mathematics. This course includes topics that are both traditionally part of a pre-university mathematics course (for example, functions, trigonometry, calculus) as well as topics that are amenable to investigation, conjecture and proof, for instance the study of sequences and series at both SL and HL, and proof by induction at HL.

The course allows the use of technology, as fluency in relevant mathematical software and hand-held technology is important regardless of choice of course. However, Mathematics: analysis and approaches has a strong emphasis on the ability to construct, communicate and justify correct mathematical arguments.

**The distinction between SL and HL**

Students who choose Mathematics: analysis and approaches at SL or HL should be comfortable in the manipulation of algebraic expressions and enjoy the recognition of patterns and understand the mathematical generalization of these patterns. Students who wish to take Mathematics: analysis and approaches at a higher level will have strong algebraic skills and the ability to understand the simple proof. They will be students who enjoy spending time with problems and get pleasure and satisfaction from solving challenging problems.

**References**

- Personal notes.
- Mathematics Analysis and Approaches for the IB Diploma, Higher Level. Ibrahim Wazir, Tim Garry. (2019), Pearson Publications.
- Mathematics: Analysis and Approaches, Higher Level. J.C.Wathall, J. Harcet, R.Harrison, L.Heinrichs, M.Torres-Skoumal. (2019), Oxford University Press.
- Mathematics Standard Level. Cirrito F., Tobin P. (2004). Ibid Press.
- Standard Level, Mathematics 2012 Edition. Wazir I., Garry T., Ashbourne P., Barclay P., Flynn P., Frederick K., Wakeford M. (2012). Pearson.
- Mathematics SL. Haese R., Haese S., Haese M., Maenpaa M., Humphries M. (2012). Haese & Harris Publications.
- Mathematics Standard Level, Course Companion. Buchanan L., Fensom J., Kemp E., Rondie P., Stevens J. (2012), Oxford University Press.
- Mathematics Standard Level, Exam Preparation Guide. Fannon P., Kadelburg V., Woolley B., Ward S. (2016), Cambridge University Press.
- Mathematics Higher Level, Exam Preparation Guide. Fannon P., Kadelburg V., Woolley B., Ward S. (2014), Cambridge University Press.