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Prospectus

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Numeracy

Course
2012-2013

Tag(s)

[BSc]
AS

Admission Requirements

None. This Academic Skills course is compulsory for all first-year students.

Description

Increasingly, government agencies, the media, and scientists report on the state of events with reference to quantitative and statistical relationships. It is all too easy to be fooled by our faulty human intuition if we don’t know how to interpret this information in an informed and thoughtful manner. The consequences of such misunderstanding can be dire. Indeed, without a sound literacy in mathematical reasoning (numeracy), it is becoming more and more difficult to be able to effectively engage in these debates critically, effectively, and responsibly. This course aims to teach students to leverage their existing mathematical techniques for thinking about real global challenges and problems through a focus on mathematically modeling phenomena relevant to these challenges.

Quantifying phenomenon and evaluating them statistically allows individuals to precisely communicate complex facts and relationships to each other that would be difficult to explain in any other way. However, if one is not skilled at avoiding key pitfalls of human intuition, being aware of certain mathematical quantities, key practices of sound scientific research design, and understanding of the foundations of statistical inference this method of communication can also be used to deceive.

This course is geared towards teaching the student how to avoid these pitfalls and consume scientific and statistical information critically. The course will focus on developing substantive understandings of key mathematical concepts and quantities, as well as foundational issues of scientific research design and statistics.

Moreover, as a foundational course for other quantitative coursework at the LUC, lessons examples, and homework will be completed within the R statistical package – even for assignments where no actual computations take place. This is done for two reasons: To help the student become familiar with computer programming and to empower the student to experiment and engage in sophisticated research projects later in the programme.

Course Objectives

The course aims to provide the students with the following skills:

  • Link numerical values and concepts to real-world scenarios, and be able to take lessons from more formal mathematical thinking to inform those real-world scenarios;

  • Develop an expanded capacity for quantitative analysis and acquiring new mathematical skills

  • Understand and critically evaluate quantitative research findings reported in scientific papers and in the media with reference to issues of research design, measurement, logic, and both substantive and statistical significance;

  • Develop a firm understanding of the empirical foundations and historical implications of probability theory, randomness, and stochasticity for problems of inference.

Mode of Instruction

Instruction in Numeracy is somewhat unique. There will be recorded lectures and/or video paired with a set of required and recommended readings. Class sessions will proceed with a portion dedicated to reviewing questions and quizzing, but will mostly be dedicated to lab work on specific exercises drawing on readings in preparation for homework assignments. Students will be expected to work in groups that will be randomly assigned each week. Students are expected to discuss their questions togetheri before seeking guidance from their lab instructor, thus functioning as tutors for each other.

Assessment

Assessment: Participation in lab seminar group
Percentage: 10%
Deadline: Weekly: Weeks 1 – 7 & 9-15

Assessment: 10 homework assignments assigned in weeks (4% each)
Percentage: 40%
Deadline: Weeks 2 – 6 & 10-14

Assessment: Final in-class written exam
Percentage: 35%
Deadline: Week 8 & Week 16

Assessment: Group Paper (max 1000 words) / Poster Presentation
Percentage: 15%
Deadline: Proposal Due week 9 & Conference in Week 16

Literature

Students will need a copy of Morris Kline’s Mathematics for the Non-mathematician as well as Course Readers prepared by the instructors.

Contact Information

b.c.zicha@luc.leidenuniv.nl:mailto:b.c.zicha@luc.leidenuniv.nl

Weekly Overview

Week 1 – Intro & Philosophy and Method of Science
Week 2 – Measurement (Numbers to Things)
Week 3 – Basic Algebra I:
Week 4 – Basic Algebra II:
Week 5 – Quantities: Logs, fractions, area and geometry, power functions, large numbers
— BE SURE to tie to underlying causal processes (concrete > abstract)
Week 6 – Differentiation and Integrals
Week 7 – Midsemester Exam Review
Week 8 – Midsemester Exam
Week 9 – Basic probability theory and sense of chance (discrete distributions)
Week 10 – Probability distributions and moments of the distribution
Week 11 – Inference & Estimates & confidence intervals
Week 12 – Hypothesis testing & Confidence Intervals
Week 13 – Regression I:
Week 14 – Regression II:
Week 15 – Final Exam Review
Week 16 – Final Exam & DAI/Numeracy Conference

Preparation for first session

Students should prepare the first sessions readings, which will consist of a number of short chapters from the reader, a video/lecture and a supplementary reading. Details will be communicated to students before the beginning of session.