STEM Quiz

STEM Education

• STEM is an umbrella term that groups together science, technology, engineering, and mathematics disciplines.
• The term is used in the context of education policy or curriculum choices in schools.
• STEM education has implications for workforce development, national security concerns, and immigration policy.

Disciplines Included in STEM

• There is no universal agreement on which disciplines are included in STEM.
• In the United States, social sciences like psychology, sociology, economics, and political science are typically included by organizations such as the National Science Foundation (NSF).
• In the United Kingdom, the inclusion of social sciences in STEM is not consistent.

Harmonic Series

• The harmonic series is an infinite series formed by summing all positive unit fractions.
• The first n terms of the series sum to approximately ln n + γ, where ln is the natural logarithm and γ ≈ 0.577 is the Euler–Mascheroni constant.
• The harmonic series is a divergent series, proven by Nicole Oresme in the 14th century using the Cauchy condensation test.
• The divergence of the harmonic series can also be proven by comparing the sum to an integral, according to the integral test for convergence.

Applications of the Harmonic Series

• The harmonic series has applications in Euler's proof that there are infinitely many prime numbers.
• It is also used in the analysis of the coupon collector's problem, which determines how many random trials are needed to provide a complete range of r.