Discrete Mathematics for GATE: A 6-Week Topic-by-Topic Study Plan

Many learners read Discrete Mathematics definitions in isolation, then freeze when one question combines a property check, a count, and a short calculation. With about 1,300 Discrete Mathematics questions available in our practice bank, the challenge is choosing practice well. Use Discrete Mathematics for GATE: Syllabus, Weightage Context and Preparation Order for official syllabus boundaries, weightage context, and the broad preparation order. Execute that map as six 8-hour weeks with theory, worked problems, timed practice, error repair, two scheduled retries, and a missed-day rule. That repeated rhythm turns a definition into a usable method, so you always know what to study and why.

1. Diagnose the gap before Week 1

Start with a 60-minute baseline of 12 genuine past-paper questions: 3 from logic, 3 from sets and relations, 2 from functions and counting, 2 from recurrences or algebraic structures, and 2 from graph theory. Record the paper and question number for each; this split balances the diagnostic and does not predict the next paper.

Suppose you score 5/12: logic 2/3, sets and relations 1/3, functions and counting 1/2, recurrence or algebra 0/2, and graphs 1/2. Classify the seven misses as 3 concept errors, 2 setup errors, 1 calculation error, and 1 time-pressure skip. Repair the concept errors first.

Use one error-log line per miss: question | topic | my wrong step | corrected rule | retry date. Retry after 2 days and again after 7 days.

2. Week 1: logic and set operations, 8 hours

Spend 2 hours on propositions, connectives, implication, equivalence, and quantifiers; 2 on truth-table drills; 2 on sets, Cartesian products, and inclusion-exclusion; 1.5 on a timed mixed set; and 30 minutes on the error log. Then use Propositional and Predicate Logic Explained for drills.

Let p = true and q = false. Then p -> q = false and not q = true, so (p -> q) and (not q) = false. Change only q to true: p -> q = true, not q = false, and the compound is still false. Follow both connectives rather than memorising a row.

For A = {1,2,3,4} and B = {3,4,5}, A union B = {1,2,3,4,5} and A intersection B = {3,4}. Thus |A union B| = 4 + 3 - 2 = 5.

3. Week 2: relations and functions, 8 hours

Allocate 2 hours to relation properties and closures, 2 to equivalence relations and partial orders, 2 to function types and composition, 1.5 to mixed problems, and 30 minutes to error repair. Turn the relation-property definitions into a checklist before practising.

Let A = {1,2,3} and R = {(1,1),(2,2),(3,3),(1,2),(2,1)}. All diagonal pairs are present, so R is reflexive. Each non-diagonal pair has its reverse, so it is symmetric. The {1,2} block contains every required composition and 3 relates only to itself, so R is transitive. It is an equivalence relation with classes {1,2} and {3}.

From a four-element domain to a two-element codomain, each input has 2 image choices, giving 2^4 = 16 functions. Exclude the 2 constant functions, one per codomain element, to get 16 - 2 = 14 onto functions.

4. Week 3: counting and recurrences, 8 hours

Use 2 hours for permutations, combinations, the pigeonhole principle, and inclusion-exclusion; 2 for recurrence setup; 2 for solution methods; 1.5 for timed questions; and 30 minutes for corrections. For a structured next resource, use the Engineering Mathematics course.

Filling 3 distinct positions from 5 candidates gives 5P3 = 5 x 4 x 3 = 60. Selecting an unordered committee gives 5C3 = (5 x 4 x 3)/(3 x 2 x 1) = 10.

Next, trace T(n) = 2T(n/2) + n, where T(1) = 1:

• T(2) = 2T(1) + 2 = 2 + 2 = 4

• T(4) = 2T(2) + 4 = 8 + 4 = 12

• T(8) = 2T(4) + 8 = 24 + 8 = 32

Write both the expansion and the final growth form, Theta(n log n).

5. Week 4: algebraic structures and graphs, 8 hours

Give 2 hours to semigroups, monoids, and groups; 1 to modular-operation tables; 2 to graph degree, paths, connectivity, trees, and planar basics; 2.5 to graph problems; and 30 minutes to the error log. Before the graph block, revise Euler trails, Hamiltonian paths, and colouring.

In Z5 = {0,1,2,3,4} under addition modulo 5, 0 is the identity. The inverse of 2 is 3 because (2 + 3) mod 5 = 0. Closure holds because results stay in Z5; for example, (4 + 3) mod 5 = 2.

For the connected graph V = {A,B,C,D} and E = {AB,BC,CD,DA,AC}, deg(A)=3, deg(B)=2, deg(C)=3, and deg(D)=2. Exactly A and C are odd, so there is an Euler trail but no Euler circuit. The trail A-B-C-D-A-C uses all five edges once.

6. Week 5: turn topic knowledge into timed PYQ patterns

Group genuine past-paper questions by operation: construct a truth table, test relation properties, count functions, apply inclusion-exclusion, solve a recurrence, or use degree and path conditions. Do not infer a fixed frequency. Name the sampled papers before calling any pattern recurring.

The budget is exact: three 50-minute mixed sets take 2.5 hours, three 40-minute reviews take 2 hours, two 90-minute repair blocks take 3 hours, and a formula-sheet update takes 30 minutes.

In a 10-question, 50-minute set, suppose 6 are correct, 2 wrong, and 2 skipped. Label one wrong answer a concept error and one a calculation error. Restate the rule for the first and find the first incorrect line for the second. After 48 hours, retry all four missed items without the solution.

7. Week 6: revise, test, and recover missed days

Take two 90-minute subject tests (3 hours), review them line by line for 2 hours, spend 2 hours on the two weakest error-log topics, and use 1 hour for a final formula and definition sheet. Finish with the GATE Test Series, then follow the wider GATE CS preparation pathway.

Recover a lost 90-minute weekday block as two 45-minute weekend blocks. Preserve error review and cut one fresh drill first. If a full 8-hour week is lost, extend the plan by one week instead of compressing 16 hours into seven days.

8. The short version

Study 8 hours a week, keep one error log, retry every miss twice, and follow prerequisite order. Take the baseline today and schedule Week 1.