Summer Courses

Credits: 3.3

Course learning outcomes:

By the end of this course, learners should be able to:

1. Solve parametrized or unparametrized systems of linear equations using Gaussian elimination and back substitution; they will be able to write the augmented matrix of a given system of linear equations, transform it into reduced or row-reduced echelon form using a sequence of elementary row operations, and finally solve the system using back substitution. They will be able to determine the number of solutions as a function of the parameter in case the system of linear equations is parametrized.
2. Perform basic matrix algebraic operations (addition, scaling, multiplication).
3. Understand the notions of eigenvalue, eigenspace, and eigenvector for a given vector space endomorphism; in particular, given a real n √ó n matrix, they will be able to compute the set of all eigenvalues of that matrix, as well as eigenvectors or bases for the eigenspaces corresponding to those eigenvalues.
4. Compute the determinant of a real n √ó n matrix and know its main properties; in particular, they will be able to use the determinant in assessing whether or not a given n √ó n matrix is invertible.
5. Prove linear algebraic results for general vector spaces; these proofs will require mathematical reasoning, will be expressed in precise mathematical language with full mathematical rigor, and will combine various notions seen in different parts of the course, such as vector subspace, linear span, linear independence, linear mapping, and eigenvalue/eigenspace/eigenvector.
6. Understand the mathematical notion of a real vector space, and will be able to determine whether or not a given subset of a real vector space is a vector subspace; in particular, students will be able to work with vector spaces other than the usual Euclidean space Rn.
7. Understand the notions of linear combination and linear span of a family of vectors, and will be able to determine whether or not a given vector is in the linear span of a given family of vectors.
8. Understand the notions of linear dependence and independence of a family of vectors, and will be able to determine whether or not a given family of vectors in a vector space is linearly independent.
9. Understand the notions of basis and dimension of a vector space; they will be able to compute a basis for a given vector space and use it to compute the dimension of the vector space.
10. Understand the notion of a linear mapping between vector spaces; in particular, they will be able to determine whether or not a given mapping between vector spaces is linear.
11. Understand the notions of kernel and image of a linear mapping; in particular, they will be able to compute the kernel and image of a given real matrix, and they will understand the precise relation between the kernel/image of a real matrix and its column vectors.

Credits: K0.2

Course learning outcomes: TBA

Credits: 3.0

Course learning outcomes:

By the end of this course, learners should be able to solve economic analysis problems:

1. Cost concepts and use a variety of cost estimation techniques.
2. Time value of money and solve cash flow analysis problems.
3. Compare a variety of projects using multiple economic approaches.
4. The effect of taxes on project viability and apply to appropriate cash flow analysis.
5. Replacement analysis concepts and apply appropriate cash flow analysis to correctly determine minimum equivalent annual costs.
6. The effect of inflation on project viability and apply to appropriate cash flow analysis.
7. Apply a variety of approaches for dealing with uncertainty and risk associated with projects.
8. Risk management approaches associated with project management.
9. Change management from an organizational behaviour perspective.
10. Recognizing new business opportunities and techniques for generating ideas.
11. Feasibility Analysis.
12. Assessing a new venture’s financial strength and viability.
13. Writing a business plan.
14. Basic management processes and concepts.

Credits: 3.5

Course learning outcomes:

By the end of this course, learners should be able to:

1. Solving basic initial value problems.
2. Solving linear constant coefficient differential equations.
3. Computing Laplace and inverse Laplace transforms.
4. Using the Laplace transform to solve differential equations.
5. Modeling a mass-spring-damper system or RLC circuit using differential equations.
6. Modeling interconnected fluid reservoirs using differential equations.

Prerequisites: APSC 171, APSC 172, APSC 174

Credits: 3.0

Course learning outcomes:

By the end of this course, learners should be able to:

1. Produce elevations from differential leveling notes.
2. Calculate coordinates and areas for survey control traverse.
3. Assess measurement for error.
4. Predict the 3-dimensional accuracy of GPA positions.
5. Produce revised ground versus grid distances for construction layout purposes.
6. Operate the main functions of Total Stations and Data Collectors.
7. Combine the main functions of Total Stations and Data Collectors to produce a pertinent report using previously gathered field data.

Credits: 3.0

Course learning outcomes:

By the end of this course, learners should be able to:

1. Describe the basic principles of rock failures.
2. Recognize appropriate field and laboratory investigation programs to define rock failure criteria.
3. Analyze data from field and laboratory investigations to define the failure criteria
4. Recognize numerical stress analysis models for excavation design
5. Use various empirical/analytical design methods for excavations such as open stopes, pillars, and open pit slopes
6. Evaluate appropriate support systems for specified ground conditions

Prerequisites: MNTC 302, APSC 182
Exclusions: MINE 325

Credits: 3.5

Course learning outcomes:

By the end of this course, learners should be able to:

1. Describe the nature and components of global minerals supply, demand, trade, and price.
2. Identify national and international policies, regulations, and treaties relevant to the minerals industry.
3. Solve structured problems using economic analysis concepts (e.g. time value of money, discounting) and financial analysis tools (e.g. Net Present Value (NPV), Internal Rate of Return (IRR), payback period).
4. Describe the estimation of mineral resources and mineral reserves, the feasibility assessment process and different types of reports, and the disclosure of the results of work in these areas under National Instrument 43-101.
5. Apply economic and financial tools to valuation of companies, evaluation of projects, and strategic planning.
6. Discover how risk and uncertainty are addressed in the techniques and processes of mineral economics.
7. Discover sources and types of equity and debt financing for mining companies and projects.
8. Examine the impact of sustainability initiatives and frameworks on mining companies and projects and ways in which sustainability is increasingly being reflected in activities studied in this course.

Prerequisites: APSC 221 and MNTC 305, or permission of the Mining Department
Exclusions: MINE 330

Credits: 3.0

Course learning outcomes:

By the end of this course, learners should be able to:

1. Explain qualitative and quantitative reliability and maintenance concepts including risk.
2. Justify the selection of maintenance policies and their appropriate applications in mining.
3. Explain the relationship between maintenance organizational structures and processes with respect to mining operations taking into account practical realities in the mining context.
4. Design maintenance organizational structures including workflow processes.
5. Apply relevant analytical techniques for the prioritization of maintenance activities and resources; including Pareto analysis, Failure Mode Analysis, and Failure Rate curves.
6. Select appropriate maintenance policies through a structured methodology (RCM), based on application of analytical techniques and incorporating costs.

Prerequisites: MNTC 302 and MNTC 304 or APSC 171, APSC 172, and APSC 182