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    An introduction to the mathematical methods used in spatial positioning and analysis. Includes concepts of measurement, least squares analysis using observation equations, transformations, spherical trigonometry and map projections.

    About this paper

    Paper title Surveying Mathematics
    Subject Surveying
    EFTS 0.1334
    Points 18 points
    Teaching period Semester 2 (On campus)
    Domestic Tuition Fees ( NZD ) $1,206.20
    International Tuition Fees Tuition Fees for international students are elsewhere on this website.
    SURV 201 or SURV 211
    Pre or Corequisite
    MATH 130
    SURV 212
    Schedule C

    Suitable for students with a good understanding of fundamental surveying methods and techniques.
    Requires an understanding of mathematical and statistical concepts.

    Teaching staff
    Lecturer: Dr Paul Denys
    Paper Structure

    The paper covers the following topics:

    • Survey measurement and spatial analysis
    • Statistical testing
    • Least squares analysis using linear observation equations
    • Least squares analysis using non-linear observation equations
    • Spherical trigonometry
    • Map projections
    Teaching Arrangements

    Lectures: Four 1-hour lectures - Monday, Tuesday, Thursday, Friday

    Tutorials: Two 1-hour tutorials - Friday



    • Denys, P. H. (2024), Computational Models for Surveying Applications


    • Cooper, M.A.R. Fundamentals of Survey Measurement and Analysis (Granada Publishing)
    • Anderson and Mikhail, (1998). Surveying Theory and Practice (7th Edition)
    Graduate Attributes Emphasised
    Scholarship, Critical thinking, Information literacy.
    View more information about Otago's graduate attributes.
    Learning Outcomes
    The goals of the paper are
    • To apply basic mathematical and statistical procedures to spatial measurement and analysis problems
    • To understand measurement errors, their sources and error propagation of a set of linear or non-linear functions
    • To establish an appropriate statistical hypothesis for a surveying-related problem and test it using the appropriate statistical distribution
    • To formulate simple observation equations, as might be needed to solve surveying applications
    • To apply non-linear least squares analysis techniques to problems in surveying practice
    • To use spherical trigonometry to be able to solve practical navigation problems
    • To understand the foundation of conformal map projection theory and be able to apply this theory to map projection problems


    Semester 2

    Teaching method
    This paper is taught On Campus
    Learning management system


    Stream Days Times Weeks
    A1 Monday 10:00-10:50 29-35, 37-42
    Tuesday 10:00-10:50 29-35, 37-42
    Thursday 10:00-10:50 29-35, 37-42
    Friday 09:00-09:50 29-35, 37-42


    Stream Days Times Weeks
    Attend one stream from
    A1 Friday 10:00-10:50 29-35, 37-42
    A2 Friday 11:00-11:50 29-35, 37-42
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