Office S616 Ross. Phone 33971
Office hours: 9:30- 10:00 MWF (in Curtis LH D), and by appointment (see me
before or after class or e-mail me).
Class MWF 8:30, Curtis Lecture Hall D.
Office: S625 Ross. Phone 66088
Class MWF 2:30, CLH E
Beginning January 23
Thursday tutorial is
4:00 - 5:00 in Ross S525 (the MathStat
Friday tutorial is 1:00-2:00 in Ross S105.
Electronic Mail List subscribe math2090
to the address:
To post to the list, send your message to
There is a electronic list for the course called:
math2090. To subscribe from the
address you wish messages sent to, send the message:
Fredrick Portoraro and Robert Tully, SYMLOG: Learning
Symbolic Logic by Computer; Prentice-Hall 1994.
There should be used copies around the campus, as it has been used
for two years. The text book comes with a PC diskette
containing as essential program. Make sure your used copy has
this diskette so you can install it at home on your PC!
Other Recommended reading : "The Logic Book" by Bermann, Moor and Nelson (McGraw Hill). This is on 2 hr. reserve in Steacie.
For further motivation and examples related to computer science, the book "A Logical Approach to Discrete Math" will also be on reserve. (Chapter 10 and Section 12.5-6 are particularly relevant.)
The SYMLOG Program
The program is installed on the ACADLABS server in Steacie.
If you plan to use it there (or if you wish to participate
in the introductory tutorial to the program in early January)
you will need to set up an ACADLAB account. Click
here for further instructions.
Course Assessment and Grading
With the program SYMLOG for assistance, you are expected to work many exercises. It is essential that you do additional problems beyond the graded assignments in order to be adept at the formal game of logic.
There will be graded assignments (about 8) worth 20% of your final grade. (Many of these questions will be done on the computer program - with an automated checker. Assignments will be marked actually marking selected parts. The main purpose of many assignment questions is to encourage you to work with the program on the computer.)
There will be two 50 minute class tests.
The first test will be around February 16. The second test will be the in mid March.
There will be a three hour final exam in the Examination Period.
The formula for the final grade will be:
20% assignments +
the maximum of [(20% tests+60% final), (60% tests+20% final)].
While these pieces will be graded with numbers, the official grades for this course are letter grades.
Math 2090 is a required course for a majority of the students in the course (computer science majors). There are specific connections between what we do in this course and several areas of computer science: program verification and program specification; data structures; artificial intelligence. However this is not a computer science course. Although examples from computer science may be used for motivation and simple exercises, no knowledge of computer science will be assumed.
The ultimate goal is to refine how you think - both formally and informally. Logic is the study of reliable (valid) arguments. When formalized these are proofs or derivations, but the same forms of argument and standards of validity apply to informal presentations. In this course you will work on different aspects of 'formal logic' as well as the connection to informal arguments. You will also be tested at several different intellectual levels.
- We will translate sentences from English (or mathematics or computer science) into formal sentences. We will also translate longer arguments from less formal settings into formal logic.
- At the core of the course is the game of 'formal logic'. There are specific rules for derivations (proofs) to be memorized and used accurately. The computer program SYMLOG will help you with this. It is very patient!
- A second level of 'doing formal logic' includes strategies for selecting which rules and formulae to use to produce a derivation (proof) for a given valid argument. This requires both practice and some judgment about what to try, when to switch to another strategy etc.. Of course, this builds on skills (i) and (ii), and will be very difficult if you cannot distinguish an incorrect argument from a correct one. Substantial skill with the symbol manipulation and the development of derivations will be tested on assignments, tests and exams.
As a companion to these 'derivations' (for valid arguments) will be 'interpretations' and 'models' which demonstrate that arguments are not valid. This includes both simple rules for interpreting a formula in a model and the more difficult judgment of which model to try. In general this process is less routine and involves more 'educated guesses' than process (iii) for derivations. However, the computer program will also help you with this - testing whether a given interpretation makes specific sentences true or false.
- The next level is 'metatheory': informal arguments about logic. For this you will memorize selected vocabulary (words like consistent, derivable, satisfiable, valid, invalid) and learn basic connections among these concepts. Some of this theory is based on the syntax (form or appearance) of what is written. Other parts of the theory are based on the semantics (meaning) of what is written. Both sides of this syntax/semantics split are important. Exercises about metatheory will be included on the assignments, tests and exams.
- The final section of the course will apply all these logical approaches to a particular form of argument in mathematics (and computer science) - mathematical induction. This section may include formal proofs using an extended version of the program (Symlog/PA). This section will also include informal inductions for simple properties and how these can be translated into the formal logic.
- The ultimate 'success' in this course would be for you to transfer the clarity and insights of the formal logic to your informal reasoning - in computer science, in mathematics and elsewhere. For example, the informal arguments of the metatheory can be transformed into the formal logic. An informal argument which would not stand up to formal analysis (which is invalid) cannot be accepted by us and should be accepted in math or in computer science. Your informal arguments in stages (iv) and
- can be improved by connecting them to the formal logic. Making such connections between the formal patterns and your own reasoning will good for both your learning and your marks.
We will directly assist you to form study groups (3-7 people) within the course. You are encouraged to work together on assignments. (List the names of all people who worked together on the front sheet, and all members will receive the same grade for the assignment.) There are significant advantages to study groups in this course:
Remember that all tests and exams will be done alone, without the computer. You should learn to check steps without assistance. The computer work and the study group will help you learn. Participation in study groups will be voluntary but you are urged to try them out and then decide.
- You will be evaluated on clear communication. This requires practice communicating with other people. The class work and the written assignments are unlikely to be sufficient practice.
- You can learn about valid arguments by arguing! If you cannot convince other people in your study group, you are unlikely to convince the markers.
In composing assignments, we will give some harder questions. Experience indicates that groups working together have more success with such questions than individuals working alone.
- With the support of a study group, we hope you will make better use of tutorials and office hours. Knowing that others are also confused on a issue should encourage you to ask for assistance (in person or electronically).
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